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Chen, Zhen; Gelb, Anne; Lee, Yoonsang Learning the dynamics for unknown hyperbolic conservation laws using deep neural networks. (English) Zbl 07816754 SIAM J. Sci. Comput. 46, No. 2, A825-A850 (2024). MSC: 65M99 65M12 65K10 35L65 62M45 68T07 PDFBibTeX XMLCite \textit{Z. Chen} et al., SIAM J. Sci. Comput. 46, No. 2, A825--A850 (2024; Zbl 07816754) Full Text: DOI
Hansen, Derek; Maddix, Danielle C.; Alizadeh, Shima; Gupta, Gaurav; Mahoney, Michael W. Learning physical models that can respect conservation laws. (English) Zbl 07808016 Physica D 457, Article ID 133952, 25 p. (2024). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M06 65N08 68Q32 62F15 62C10 49M41 35L65 35L67 62D05 PDFBibTeX XMLCite \textit{D. Hansen} et al., Physica D 457, Article ID 133952, 25 p. (2024; Zbl 07808016) Full Text: DOI arXiv
Charles, Philip; Ray, Deep Learning WENO for entropy stable schemes to solve conservation laws. arXiv:2403.14848 Preprint, arXiv:2403.14848 [math.NA] (2024). MSC: 65M06 65M12 35L65 68T07 BibTeX Cite \textit{P. Charles} and \textit{D. Ray}, ``Learning WENO for entropy stable schemes to solve conservation laws'', Preprint, arXiv:2403.14848 [math.NA] (2024) Full Text: arXiv OA License
Caldana, Matteo; Antonietti, Paola F.; Dede’, Luca Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning. arXiv:2402.16517 Preprint, arXiv:2402.16517 [math.NA] (2024). MSC: 35L65 65M60 68T01 BibTeX Cite \textit{M. Caldana} et al., ``Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning'', Preprint, arXiv:2402.16517 [math.NA] (2024) Full Text: arXiv OA License
Bendimerad-Hohl, Antoine; Matignon, Denis; Haine, Ghislain; Lefèvre, Laurent On implicit and explicit representations for 1D distributed port-Hamiltonian systems. arXiv:2402.07628 Preprint, arXiv:2402.07628 [math.DS] (2024). MSC: 37K06 68M14 BibTeX Cite \textit{A. Bendimerad-Hohl} et al., ``On implicit and explicit representations for 1D distributed port-Hamiltonian systems'', Preprint, arXiv:2402.07628 [math.DS] (2024) Full Text: arXiv OA License
Huang, Haoxiang; Yang, Vigor; Liu, Yingjie Neural networks with local converging inputs (NNLCI) for solving conservation laws. II: 2D problems. (English) Zbl 07783914 Commun. Comput. Phys. 34, No. 4, 907-933 (2023). MSC: 65L99 65M99 65N99 68T99 76L05 PDFBibTeX XMLCite \textit{H. Huang} et al., Commun. Comput. Phys. 34, No. 4, 907--933 (2023; Zbl 07783914) Full Text: DOI
Hillebrand, Dorian; Klein, Simon-Christian; Öffner, Philipp Applications of limiters, neural networks and polynomial annihilation in higher-order FD/FV schemes. (English) Zbl 07742012 J. Sci. Comput. 97, No. 1, Paper No. 13, 31 p. (2023). MSC: 65M08 65M06 65N08 65L06 68T07 35L65 76N15 PDFBibTeX XMLCite \textit{D. Hillebrand} et al., J. Sci. Comput. 97, No. 1, Paper No. 13, 31 p. (2023; Zbl 07742012) Full Text: DOI OA License
Huang, Haoxiang; Yang, Vigor; Liu, Yingjie Neural networks with local converging inputs (NNLCI) for solving conservation laws. I: 1D problems. (English) Zbl 1519.65018 Commun. Comput. Phys. 34, No. 2, 290-317 (2023). MSC: 65L99 35L65 68T07 76L05 76M20 PDFBibTeX XMLCite \textit{H. Huang} et al., Commun. Comput. Phys. 34, No. 2, 290--317 (2023; Zbl 1519.65018) Full Text: DOI
Hydon, P. E. Partial Euler operators and the efficient inversion of Div. (English) Zbl 1522.35011 Eur. J. Appl. Math. 34, No. 5, 1046-1066 (2023). MSC: 35A15 35B06 68W30 PDFBibTeX XMLCite \textit{P. E. Hydon}, Eur. J. Appl. Math. 34, No. 5, 1046--1066 (2023; Zbl 1522.35011) Full Text: DOI arXiv OA License
Moudgalya, Sanjay; Motrunich, Olexei I. From symmetries to commutant algebras in standard Hamiltonians. (English) Zbl 1528.81229 Ann. Phys. 455, Article ID 169384, 50 p. (2023). MSC: 81V70 22E70 05E40 46C05 70H05 81R25 81V74 37K06 68P10 PDFBibTeX XMLCite \textit{S. Moudgalya} and \textit{O. I. Motrunich}, Ann. Phys. 455, Article ID 169384, 50 p. (2023; Zbl 1528.81229) Full Text: DOI arXiv
Cardall, Christian Y.; Budiardja, Reuben D. GenASiS Mathematics: object-oriented manifolds, operations, and solvers for large-scale physics simulations (version 2). (English) Zbl 07692482 Comput. Phys. Commun. 282, Article ID 108518, 3 p. (2023). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{C. Y. Cardall} and \textit{R. D. Budiardja}, Comput. Phys. Commun. 282, Article ID 108518, 3 p. (2023; Zbl 07692482) Full Text: DOI
Strelow, Erik Laurin; Gerisch, Alf; Lang, Jens; Pfetsch, Marc E. Physics informed neural networks: a case study for gas transport problems. (English) Zbl 07679162 J. Comput. Phys. 481, Article ID 112041, 16 p. (2023). MSC: 65Mxx 68Txx 65-XX PDFBibTeX XMLCite \textit{E. L. Strelow} et al., J. Comput. Phys. 481, Article ID 112041, 16 p. (2023; Zbl 07679162) Full Text: DOI
Rasin, Alexander G. Computation of generating symmetries. (English) Zbl 1511.37074 Commun. Nonlinear Sci. Numer. Simul. 118, Article ID 107003, 12 p. (2023). MSC: 37K06 37-04 37K10 35B06 35Q51 70G65 70H33 70S10 68W30 PDFBibTeX XMLCite \textit{A. G. Rasin}, Commun. Nonlinear Sci. Numer. Simul. 118, Article ID 107003, 12 p. (2023; Zbl 1511.37074) Full Text: DOI arXiv
Aceto, Lidia; Grassi, Pietro Antonio A charge-preserving method for solving graph neural diffusion networks. arXiv:2312.10279 Preprint, arXiv:2312.10279 [math.NA] (2023). MSC: 68T07 70H33 37J06 65P99 65L05 BibTeX Cite \textit{L. Aceto} and \textit{P. A. Grassi}, ``A charge-preserving method for solving graph neural diffusion networks'', Preprint, arXiv:2312.10279 [math.NA] (2023) Full Text: arXiv OA License
Otto, Samuel E.; Zolman, Nicholas; Kutz, J. Nathan; Brunton, Steven L. A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning. arXiv:2311.00212 Preprint, arXiv:2311.00212 [cs.LG] (2023). MSC: 15B30 22E15 22E70 47D03 54H15 57S99 58D19 58K70 65F55 68Q32 68T07 70G65 70H33 90C25 BibTeX Cite \textit{S. E. Otto} et al., ``A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning'', Preprint, arXiv:2311.00212 [cs.LG] (2023) Full Text: arXiv OA License
Schwerdtner, Paul; Schulze, Philipp; Berman, Jules; Peherstorfer, Benjamin Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes. arXiv:2310.07485 Preprint, arXiv:2310.07485 [math.NA] (2023). MSC: 65M22 65P10 68T07 70H33 BibTeX Cite \textit{P. Schwerdtner} et al., ``Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes'', Preprint, arXiv:2310.07485 [math.NA] (2023) Full Text: arXiv OA License
Mukherjee, Purba; Said, Jackson Levi; Mifsud, Jurgen Neural network reconstruction of \(H^\prime(z)\) and its application in teleparallel gravity. (English) Zbl 1519.83026 J. Cosmol. Astropart. Phys. 2022, No. 12, Paper No. 29, 27 p. (2022). MSC: 83C40 83D05 53B15 70H45 76A15 68T07 83B05 PDFBibTeX XMLCite \textit{P. Mukherjee} et al., J. Cosmol. Astropart. Phys. 2022, No. 12, Paper No. 29, 27 p. (2022; Zbl 1519.83026) Full Text: DOI
Unnikrishnan, C. S. New relativity in the gravitational universe. The theory of cosmic relativity and its experimental evidence. (English) Zbl 1519.83028 Fundamental Theories of Physics 209. Cham: Springer (ISBN 978-3-031-08934-3/hbk; 978-3-031-08937-4/pbk; 978-3-031-08935-0/ebook). xxi, 485 p. (2022). MSC: 83C40 83F05 83C10 68N19 00A79 83-01 PDFBibTeX XMLCite \textit{C. S. Unnikrishnan}, New relativity in the gravitational universe. The theory of cosmic relativity and its experimental evidence. Cham: Springer (2022; Zbl 1519.83028) Full Text: DOI
Frasca-Caccia, Gianluca; Hydon, Peter E. A new technique for preserving conservation laws. (English) Zbl 1492.65235 Found. Comput. Math. 22, No. 2, 477-506 (2022). MSC: 65M06 65M22 65D32 37K06 39A14 68W30 35C08 35Q35 PDFBibTeX XMLCite \textit{G. Frasca-Caccia} and \textit{P. E. Hydon}, Found. Comput. Math. 22, No. 2, 477--506 (2022; Zbl 1492.65235) Full Text: DOI arXiv
Patel, Ravi G.; Manickam, Indu; Trask, Nathaniel A.; Wood, Mitchell A.; Lee, Myoungkyu; Tomas, Ignacio; Cyr, Eric C. Thermodynamically consistent physics-informed neural networks for hyperbolic systems. (English) Zbl 07524762 J. Comput. Phys. 449, Article ID 110754, 24 p. (2022). MSC: 35Lxx 65Mxx 68Txx PDFBibTeX XMLCite \textit{R. G. Patel} et al., J. Comput. Phys. 449, Article ID 110754, 24 p. (2022; Zbl 07524762) Full Text: DOI arXiv
Giri, Kinsuk; Rudra, Prabir Constraints on cubic and \(f(P)\) gravity from the cosmic chronometers, BAO & CMB datasets: use of machine learning algorithms. (English) Zbl 1495.83071 Nucl. Phys., B 978, Article ID 115746, 23 p. (2022). MSC: 83F05 83C05 83D05 83C40 70H45 32T40 65C05 78A45 62H20 68T05 82C32 PDFBibTeX XMLCite \textit{K. Giri} and \textit{P. Rudra}, Nucl. Phys., B 978, Article ID 115746, 23 p. (2022; Zbl 1495.83071) Full Text: DOI arXiv
Guo, Xu; Wang, Jiansen; Yang, Senlin; Ren, Yuxiao Optimal staggered-grid finite-difference method for wave modeling based on artificial neural networks. (English) Zbl 1524.65343 Comput. Math. Appl. 108, 141-158 (2022). MSC: 65M06 86A15 65M60 68T05 35L65 65K10 PDFBibTeX XMLCite \textit{X. Guo} et al., Comput. Math. Appl. 108, 141--158 (2022; Zbl 1524.65343) Full Text: DOI
Boreale, Michele; Collodi, Luisa A linear-algebraic method to compute polynomial PDE conservation laws. (English) Zbl 1475.35124 J. Symb. Comput. 108, 55-72 (2022). MSC: 35G50 35L65 68W30 PDFBibTeX XMLCite \textit{M. Boreale} and \textit{L. Collodi}, J. Symb. Comput. 108, 55--72 (2022; Zbl 1475.35124) Full Text: DOI
Moroke, M. C.; Muatjetjeja, B.; Adem, A. R. A generalized (2 + 1)-dimensional Calogaro-Bogoyavlenskii-Schiff equation: symbolic computation, symmetry reductions, exact solutions, conservation laws. (English) Zbl 1485.35099 Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 134, 15 p. (2021). MSC: 35C05 35B06 35G25 68W30 PDFBibTeX XMLCite \textit{M. C. Moroke} et al., Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 134, 15 p. (2021; Zbl 1485.35099) Full Text: DOI
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael Enhanced fifth order WENO shock-capturing schemes with deep learning. (English) Zbl 1481.65136 Results Appl. Math. 12, Article ID 100201, 20 p. (2021). MSC: 65M06 65N06 68T07 76L05 35Q31 35Q53 PDFBibTeX XMLCite \textit{T. Kossaczká} et al., Results Appl. Math. 12, Article ID 100201, 20 p. (2021; Zbl 1481.65136) Full Text: DOI arXiv
Gao, Zhen; Liu, Qi; Hesthaven, Jan S.; Wang, Bao-Shan; Don, Wai Sun; Wen, Xiao Non-intrusive reduced order modeling of convection dominated flows using artificial neural networks with application to Rayleigh-Taylor instability. (English) Zbl 1528.65070 Commun. Comput. Phys. 30, No. 1, 97-123 (2021). MSC: 65M60 65M99 65D12 65L04 65L06 68T07 76N15 76L05 76E17 76E30 35L65 35Q35 PDFBibTeX XMLCite \textit{Z. Gao} et al., Commun. Comput. Phys. 30, No. 1, 97--123 (2021; Zbl 1528.65070) Full Text: DOI
Boso, Francesca; Boskos, Dimitris; Cortés, Jorge; Martínez, Sonia; Tartakovsky, Daniel M. Dynamics of data-driven ambiguity sets for hyperbolic conservation laws with uncertain inputs. (English) Zbl 1467.35366 SIAM J. Sci. Comput. 43, No. 3, A2102-A2129 (2021). MSC: 35R60 35L65 60H15 68T37 90C15 90C90 PDFBibTeX XMLCite \textit{F. Boso} et al., SIAM J. Sci. Comput. 43, No. 3, A2102--A2129 (2021; Zbl 1467.35366) Full Text: DOI arXiv
Sokolov, A. V. Generic energy transport solutions to the solar abundance problem – a hint of new physics. (English) Zbl 1490.85010 J. Cosmol. Astropart. Phys. 2020, No. 3, Paper No. 13, 33 p. (2020). MSC: 85A25 85A15 83C40 68T37 82C70 81V15 35B38 47A10 81V80 83C56 80A10 82D75 PDFBibTeX XMLCite \textit{A. V. Sokolov}, J. Cosmol. Astropart. Phys. 2020, No. 3, Paper No. 13, 33 p. (2020; Zbl 1490.85010) Full Text: DOI arXiv
Wang, Yufei; Shen, Ziju; Long, Zichao; Dong, Bin Learning to discretize: solving 1D scalar conservation laws via deep reinforcement learning. (English) Zbl 1473.65124 Commun. Comput. Phys. 28, No. 5, 2158-2179 (2020). MSC: 65M06 68T05 49N90 PDFBibTeX XMLCite \textit{Y. Wang} et al., Commun. Comput. Phys. 28, No. 5, 2158--2179 (2020; Zbl 1473.65124) Full Text: DOI arXiv
Sun, Zheng; Wang, Shuyi; Chang, Lo-Bin; Xing, Yulong; Xiu, Dongbin Convolution neural network shock detector for numerical solution of conservation laws. (English) Zbl 1528.65092 Commun. Comput. Phys. 28, No. 5, 2075-2108 (2020). MSC: 65M99 65M06 65N06 35L65 35L67 68T07 PDFBibTeX XMLCite \textit{Z. Sun} et al., Commun. Comput. Phys. 28, No. 5, 2075--2108 (2020; Zbl 1528.65092) Full Text: DOI
Cordesse, Pierre; Massot, Marc Entropy supplementary conservation law for non-linear systems of PDEs with non-conservative terms: application to the modelling and analysis of complex fluid flows using computer algebra. (English) Zbl 1460.35225 Commun. Math. Sci. 18, No. 2, 515-534 (2020). MSC: 35L65 35L60 68W30 76N15 76T10 82D10 PDFBibTeX XMLCite \textit{P. Cordesse} and \textit{M. Massot}, Commun. Math. Sci. 18, No. 2, 515--534 (2020; Zbl 1460.35225) Full Text: DOI arXiv
Fischer, Michael; Jankowiak, Gaspard; Wolfram, Marie-Therese Micro- and macroscopic modeling of crowding and pushing in corridors. (English) Zbl 1455.91175 Netw. Heterog. Media 15, No. 3, 405-426 (2020). MSC: 91C99 76A30 68Q80 35Q84 PDFBibTeX XMLCite \textit{M. Fischer} et al., Netw. Heterog. Media 15, No. 3, 405--426 (2020; Zbl 1455.91175) Full Text: DOI arXiv
Batkhin, A. B. Bifurcations of periodic solutions of a Hamiltonian system with a discrete symmetry group. (English. Russian original) Zbl 1459.37042 Program. Comput. Softw. 46, No. 2, 84-97 (2020); translation from Programmirovanie 46, No. 2, 14-29 (2020). MSC: 37J20 37J46 37J11 65P30 70H33 68W30 PDFBibTeX XMLCite \textit{A. B. Batkhin}, Program. Comput. Softw. 46, No. 2, 84--97 (2020; Zbl 1459.37042); translation from Programmirovanie 46, No. 2, 14--29 (2020) Full Text: DOI
Bruno, A. D. Normalization of a periodic Hamiltonian system. (English. Russian original) Zbl 1459.37048 Program. Comput. Softw. 46, No. 2, 76-83 (2020); translation from Programmirovanie 46, No. 2, 6-13 (2020). MSC: 37J40 34C20 70H05 70H33 68W30 PDFBibTeX XMLCite \textit{A. D. Bruno}, Program. Comput. Softw. 46, No. 2, 76--83 (2020; Zbl 1459.37048); translation from Programmirovanie 46, No. 2, 6--13 (2020) Full Text: DOI
Holm, Håvard H.; Sætra, Martin L.; Brodtkorb, André R. Data assimilation for ocean drift trajectories using massive ensembles and GPUs. (English) Zbl 1454.65089 Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 715-723 (2020). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65N08 62M99 60G35 35L65 76B15 68N19 65Y10 65Y05 86A05 PDFBibTeX XMLCite \textit{H. H. Holm} et al., Springer Proc. Math. Stat. 323, 715--723 (2020; Zbl 1454.65089) Full Text: DOI Link
Magiera, Jim; Ray, Deep; Hesthaven, Jan S.; Rohde, Christian Constraint-aware neural networks for Riemann problems. (English) Zbl 1435.76046 J. Comput. Phys. 409, Article ID 109345, 27 p. (2020). MSC: 76M12 35L65 68T07 PDFBibTeX XMLCite \textit{J. Magiera} et al., J. Comput. Phys. 409, Article ID 109345, 27 p. (2020; Zbl 1435.76046) Full Text: DOI arXiv
Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems. (English) Zbl 1442.92002 Comput. Methods Appl. Mech. Eng. 365, Article ID 113028, 26 p. (2020). MSC: 92B20 92-08 65M99 68T07 76D05 PDFBibTeX XMLCite \textit{A. D. Jagtap} et al., Comput. Methods Appl. Mech. Eng. 365, Article ID 113028, 26 p. (2020; Zbl 1442.92002) Full Text: DOI
Feng, Yiwei; Liu, Tiegang; Wang, Kun A characteristic-featured shock wave indicator for conservation laws based on training an artificial neuron. (English) Zbl 1437.65136 J. Sci. Comput. 83, No. 1, Paper No. 21, 34 p. (2020). MSC: 65M60 65L06 68Q32 68T07 35L67 35Q53 PDFBibTeX XMLCite \textit{Y. Feng} et al., J. Sci. Comput. 83, No. 1, Paper No. 21, 34 p. (2020; Zbl 1437.65136) Full Text: DOI
Ray, Deep; Hesthaven, Jan S. Detecting troubled-cells on two-dimensional unstructured grids using a neural network. (English) Zbl 1453.65301 J. Comput. Phys. 397, Article ID 108845, 31 p. (2019). MSC: 65M50 68T07 65M60 76M10 35L65 PDFBibTeX XMLCite \textit{D. Ray} and \textit{J. S. Hesthaven}, J. Comput. Phys. 397, Article ID 108845, 31 p. (2019; Zbl 1453.65301) Full Text: DOI Link
Lang, Lukas F. A numerical framework for efficient motion estimation on evolving sphere-like surfaces based on brightness and mass conservation laws. (English) Zbl 1437.35490 SIAM J. Imaging Sci. 12, No. 1, 459-491 (2019). MSC: 35L65 33C55 35A15 53A05 65M60 68U10 92C37 92C55 PDFBibTeX XMLCite \textit{L. F. Lang}, SIAM J. Imaging Sci. 12, No. 1, 459--491 (2019; Zbl 1437.35490) Full Text: DOI arXiv
Qin, Chun-Yan; Tian, Shou-Fu; Wang, Xiu-Bin; Zou, Li; Zhang, Tian-Tian Lie symmetry analysis, conservation laws and analytic solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation. (English) Zbl 07820326 Chin. J. Phys., Taipei 56, No. 4, 1734-1742 (2018). MSC: 35Q51 35Q53 35C99 68W30 74J35 PDFBibTeX XMLCite \textit{C.-Y. Qin} et al., Chin. J. Phys., Taipei 56, No. 4, 1734--1742 (2018; Zbl 07820326) Full Text: DOI
Cardall, Christian Y.; Budiardja, Reuben D. GenASiS Mathematics: object-oriented manifolds, operations, and solvers for large-scale physics simulations. (English) Zbl 07693058 Comput. Phys. Commun. 222, 384-412 (2018). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{C. Y. Cardall} and \textit{R. D. Budiardja}, Comput. Phys. Commun. 222, 384--412 (2018; Zbl 07693058) Full Text: DOI arXiv
Lan, Zhongzhou; Gao, Bo Lax pair, infinitely many conservation laws and solitons for a \((2 + 1)\)-dimensional Heisenberg ferromagnetic spin chain equation with time-dependent coefficients. (English) Zbl 1459.82338 Appl. Math. Lett. 79, 6-12 (2018). MSC: 82D40 82B20 37K06 37K35 37K40 35C08 68W30 35Q55 35Q82 PDFBibTeX XMLCite \textit{Z. Lan} and \textit{B. Gao}, Appl. Math. Lett. 79, 6--12 (2018; Zbl 1459.82338) Full Text: DOI
Ray, Deep; Hesthaven, Jan S. An artificial neural network as a troubled-cell indicator. (English) Zbl 1415.65229 J. Comput. Phys. 367, 166-191 (2018). MSC: 65M60 35L65 68T05 PDFBibTeX XMLCite \textit{D. Ray} and \textit{J. S. Hesthaven}, J. Comput. Phys. 367, 166--191 (2018; Zbl 1415.65229) Full Text: DOI Link
Wang, Xiu-Bin; Tian, Shou-Fu Lie symmetry analysis, conservation laws and analytical solutions of the time-fractional thin-film equation. (English) Zbl 1413.35395 Comput. Appl. Math. 37, No. 5, 6270-6282 (2018). MSC: 35Q51 35Q53 35C99 68W30 74J35 PDFBibTeX XMLCite \textit{X.-B. Wang} and \textit{S.-F. Tian}, Comput. Appl. Math. 37, No. 5, 6270--6282 (2018; Zbl 1413.35395) Full Text: DOI
Essadki, Mohamed; Jung, Jonathan; Larat, Adam; Pelletier, Milan; Perrier, Vincent A task-driven implementation of a simple numerical solver for hyperbolic conservation laws. (English. French summary) Zbl 1408.65061 ESAIM, Proc. Surv. 63, 228-247 (2018). MSC: 65M08 65M06 65Y05 65Y10 68M10 90B18 PDFBibTeX XMLCite \textit{M. Essadki} et al., ESAIM, Proc. Surv. 63, 228--247 (2018; Zbl 1408.65061) Full Text: DOI arXiv
Li, Tong; Park, Jeungeun Stability of traveling waves of models for image processing with non-convex nonlinearity. (English) Zbl 1394.35034 Commun. Pure Appl. Anal. 17, No. 3, 959-985 (2018). MSC: 35B35 35B40 35B45 35C07 35L65 68U10 PDFBibTeX XMLCite \textit{T. Li} and \textit{J. Park}, Commun. Pure Appl. Anal. 17, No. 3, 959--985 (2018; Zbl 1394.35034) Full Text: DOI
Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian Lie symmetry analysis, conservation laws and analytical solutions of a time-fractional generalized KdV-type equation. (English) Zbl 1420.35298 J. Nonlinear Math. Phys. 24, No. 4, 516-530 (2017). MSC: 35Q51 35Q53 35C99 68W30 74J35 PDFBibTeX XMLCite \textit{X.-B. Wang} et al., J. Nonlinear Math. Phys. 24, No. 4, 516--530 (2017; Zbl 1420.35298) Full Text: DOI
Koppenol, Daniël C.; Vermolen, Fred J.; Koppenol-Gonzalez, Gabriela V.; Niessen, Frank B.; van Zuijlen, Paul P. M.; Vuik, Kees A mathematical model for the simulation of the contraction of burns. (English) Zbl 1373.35319 J. Math. Biol. 75, No. 1, 1-31 (2017). MSC: 35Q92 35L65 35M10 62H15 62J05 62P30 65C20 68U20 74L15 92C10 92C17 65M20 65N30 PDFBibTeX XMLCite \textit{D. C. Koppenol} et al., J. Math. Biol. 75, No. 1, 1--31 (2017; Zbl 1373.35319) Full Text: DOI
Zhang, Zhi-Yong; Guo, Lei-Lei; Huang, Ji-Zheng The four-dimensional Martínez Alonso-Shabat equation: nonlinear self-adjointness and conservation laws. (English) Zbl 1361.35014 Math. Methods Appl. Sci. 40, No. 1, 84-91 (2017). MSC: 35A30 70S10 35B06 68W30 PDFBibTeX XMLCite \textit{Z.-Y. Zhang} et al., Math. Methods Appl. Sci. 40, No. 1, 84--91 (2017; Zbl 1361.35014) Full Text: DOI
Adem, Abdullahi Rashid; Khalique, Chaudry Masood Symbolic computation of conservation laws and exact solutions of a coupled variable-coefficient modified Korteweg-de Vries system. (English) Zbl 1352.35145 Comput. Math. Math. Phys. 56, No. 4, 650-660 (2016). MSC: 35Q53 35C05 68W30 35Q86 86A10 PDFBibTeX XMLCite \textit{A. R. Adem} and \textit{C. M. Khalique}, Comput. Math. Math. Phys. 56, No. 4, 650--660 (2016; Zbl 1352.35145) Full Text: DOI
El-Taha, Muhammad Invariance of workload in queueing systems. (English) Zbl 1341.60113 Queueing Syst. 83, No. 1-2, 181-192 (2016). MSC: 60K25 90B22 68M20 PDFBibTeX XMLCite \textit{M. El-Taha}, Queueing Syst. 83, No. 1--2, 181--192 (2016; Zbl 1341.60113) Full Text: DOI
Castro, Douglas A.; Gomes, Sônia M.; Stolfi, Jorge High-order adaptive finite-volume schemes in the context of multiresolution analysis for dyadic grids. (English) Zbl 1338.76074 Comput. Appl. Math. 35, No. 1, 1-16 (2016). MSC: 76M12 65T60 68P05 35L65 PDFBibTeX XMLCite \textit{D. A. Castro} et al., Comput. Appl. Math. 35, No. 1, 1--16 (2016; Zbl 1338.76074) Full Text: DOI
Ramírez, J.; Romero, Juan Luis; Muriel, Concepcion Reductions of PDEs to first order ODEs, symmetries and symbolic computation. (English) Zbl 1510.35018 Commun. Nonlinear Sci. Numer. Simul. 29, No. 1-3, 37-49 (2015). MSC: 35A30 37K06 68W30 PDFBibTeX XMLCite \textit{J. Ramírez} et al., Commun. Nonlinear Sci. Numer. Simul. 29, No. 1--3, 37--49 (2015; Zbl 1510.35018) Full Text: DOI
Canic, Suncica; Piccoli, Benedetto; Qiu, Jing-Mei; Ren, Tan Runge-Kutta discontinuous Galerkin method for traffic flow model on networks. (English) Zbl 1321.90034 J. Sci. Comput. 63, No. 1, 233-255 (2015). MSC: 90B20 90B06 90B15 68U20 PDFBibTeX XMLCite \textit{S. Canic} et al., J. Sci. Comput. 63, No. 1, 233--255 (2015; Zbl 1321.90034) Full Text: DOI arXiv
Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations. (English) Zbl 1330.76088 J. Sci. Comput. 63, No. 1, 23-48 (2015). MSC: 76M12 65M08 76B15 35L65 65M50 65Y10 68N19 PDFBibTeX XMLCite \textit{M. L. Sætra} et al., J. Sci. Comput. 63, No. 1, 23--48 (2015; Zbl 1330.76088) Full Text: DOI
Cheviakov, Alexei F. Symbolic computation of nonlocal symmetries and nonlocal conservation laws of partial differential equations using the GeM package for Maple. (English) Zbl 1309.74075 Ganghoffer, Jean-François (ed.) et al., Similarity and symmetry methods. Applications in elasticity and mechanics of materials. Lecture notes given at the EUROMECH workshop ‘Similarity, symmetry and group theoretical methods in mechanics, Varna, Bulgaria, June 6–9, 2013. Cham: Springer (ISBN 978-3-319-08295-0/hbk; 978-3-319-08296-7/ebook). Lecture Notes in Applied and Computational Mechanics 73, 165-184 (2014). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 74S30 68W30 35L65 35Q74 PDFBibTeX XMLCite \textit{A. F. Cheviakov}, Lect. Notes Appl. Comput. Mech. 73, 165--184 (2014; Zbl 1309.74075) Full Text: DOI
Atkey, Robert From parametricity to conservation laws, via Noether’s theorem. (English) Zbl 1284.68162 Proceedings of the 41st ACM SIGPLAN-SIGACT symposium on principles of programming languages, POPL ’14, San Diego, CA, USA, January 22–24, 2014. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2544-8). 491-502 (2014). MSC: 68N30 03B70 70A05 70H03 PDFBibTeX XMLCite \textit{R. Atkey}, in: Proceedings of the 41st ACM SIGPLAN-SIGACT symposium on principles of programming languages, POPL '14, San Diego, CA, USA, January 22--24, 2014. New York, NY: Association for Computing Machinery (ACM). 491--502 (2014; Zbl 1284.68162) Full Text: DOI Link
Naz, Rehana; Naeem, Imran; Khan, M. Danish Conservation laws of some physical models via symbolic package GeM. (English) Zbl 1299.35001 Math. Probl. Eng. 2013, Article ID 897912, 7 p. (2013). MSC: 35-04 35L65 35A30 68W30 PDFBibTeX XMLCite \textit{R. Naz} et al., Math. Probl. Eng. 2013, Article ID 897912, 7 p. (2013; Zbl 1299.35001) Full Text: DOI
Zhu, Jiaofeng; Liu, Yinping Automated derivation of the conservation laws for nonlinear differential-difference equations. (English) Zbl 1286.34020 J. Syst. Sci. Complex. 25, No. 6, 1234-1248 (2012). MSC: 34A33 34A45 34-04 68T15 PDFBibTeX XMLCite \textit{J. Zhu} and \textit{Y. Liu}, J. Syst. Sci. Complex. 25, No. 6, 1234--1248 (2012; Zbl 1286.34020) Full Text: DOI
Kaptsov, O. V. On the Goursat classification problem. (English. Russian original) Zbl 1255.35165 Program. Comput. Softw. 38, No. 2, 102-104 (2012); translation from Programmirovanie 38, No. 2 (2012). MSC: 35L65 68W30 35L70 PDFBibTeX XMLCite \textit{O. V. Kaptsov}, Program. Comput. Softw. 38, No. 2, 102--104 (2012; Zbl 1255.35165); translation from Programmirovanie 38, No. 2 (2012) Full Text: DOI
Tricoche, Xavier; Garth, Christoph; Sanderson, Allen; Joy, Ken Visualizing invariant manifolds in area-preserving maps. (English) Zbl 1248.68159 Peikert, Ronald (ed.) et al., Topological methods in data analysis and visualization II. Theory, algorithms, and applications. Based on the 4th workshop on topology-based methods in data analysis and visualization, TopoInVis 2011, Zurich, Switzerland, April 4–6, 2011. Berlin: Springer (ISBN 978-3-642-23174-2/hbk; 978-3-642-23175-9/ebook). Mathematics and Visualization, 109-124 (2012). MSC: 68N99 37K05 PDFBibTeX XMLCite \textit{X. Tricoche} et al., in: Topological methods in data analysis and visualization II. Theory, algorithms, and applications. Based on the 4th workshop on topology-based methods in data analysis and visualization, TopoInVis 2011, Zurich, Switzerland, April 4--6, 2011. Berlin: Springer. 109--124 (2012; Zbl 1248.68159) Full Text: DOI
Göktaş, Ünal; Hereman, Willy Symbolic computation of conservation laws, generalized symmetries, and recursion operators for nonlinear differential-difference equations. (English) Zbl 1245.34001 Luo, Albert C.J. (ed.) et al., Dynamical systems and methods. Based on the 3rd conference on nonlinear science and complexity (NSC), Ankara, Turkey, July 27–31, 2010. Berlin: Springer (ISBN 978-1-4614-0453-8/hbk; 978-1-4614-0454-5/ebook). 153-168 (2012). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 34-04 34A33 34A05 34C14 68W30 PDFBibTeX XMLCite \textit{Ü. Göktaş} and \textit{W. Hereman}, in: Dynamical systems and methods. Based on the 3rd conference on nonlinear science and complexity (NSC), Ankara, Turkey, July 27--31, 2010. Berlin: Springer. 153--168 (2012; Zbl 1245.34001) Full Text: DOI arXiv
Yu, Xin; Gao, Yi-Tian; Sun, Zhi-Yuan; Liu, Ying Infinite sequence of conservation laws and analytic solutions for a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids. (English) Zbl 1264.35204 Commun. Theor. Phys. 55, No. 4, 629-634 (2011). MSC: 35Q53 76B15 35Q35 76B25 35C08 35N10 35L65 68W30 PDFBibTeX XMLCite \textit{X. Yu} et al., Commun. Theor. Phys. 55, No. 4, 629--634 (2011; Zbl 1264.35204) Full Text: DOI
Formenti, Enrico; Kari, Jarkko; Taati, Siamak On the hierarchy of conservation laws in a cellular automaton. (English) Zbl 1251.68148 Nat. Comput. 10, No. 4, 1275-1294 (2011). MSC: 68Q80 37B15 PDFBibTeX XMLCite \textit{E. Formenti} et al., Nat. Comput. 10, No. 4, 1275--1294 (2011; Zbl 1251.68148) Full Text: DOI
Poole, Douglas; Hereman, Willy Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions. (English) Zbl 1234.35071 J. Symb. Comput. 46, No. 12, 1355-1377 (2011). MSC: 35G20 68W30 37K10 PDFBibTeX XMLCite \textit{D. Poole} and \textit{W. Hereman}, J. Symb. Comput. 46, No. 12, 1355--1377 (2011; Zbl 1234.35071) Full Text: DOI arXiv
Irtegov, Valentin; Titorenko, Tatyana On invariant manifolds of Lagrange systems. (English) Zbl 1308.70034 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 13th international workshop, CASC 2011, Kassel, Germany, September 5–9, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-23567-2/pbk). Lecture Notes in Computer Science 6885, 226-238 (2011). MSC: 70H33 68W30 PDFBibTeX XMLCite \textit{V. Irtegov} and \textit{T. Titorenko}, Lect. Notes Comput. Sci. 6885, 226--238 (2011; Zbl 1308.70034) Full Text: DOI
Rocha Filho, Tarcísio M.; Figueiredo, Annibal [SADE] a Maple package for the symmetry analysis of differential equations. (English) Zbl 1217.65165 Comput. Phys. Commun. 182, No. 2, 467-476 (2011). MSC: 65L99 34C14 68W30 65Y15 PDFBibTeX XMLCite \textit{T. M. Rocha Filho} and \textit{A. Figueiredo}, Comput. Phys. Commun. 182, No. 2, 467--476 (2011; Zbl 1217.65165) Full Text: DOI arXiv
Sankaranarayanan, Sriram Automatic invariant generation for hybrid systems using ideal fixed points. (English) Zbl 1360.34082 Proceedings of the 13th ACM international conference on hybrid systems: computation and control, HSCC 2010, Stockholm, Sweden, April 12–16, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-955-8). 221-230 (2010). MSC: 34C14 13N10 34A38 68Q60 PDFBibTeX XMLCite \textit{S. Sankaranarayanan}, in: Proceedings of the 13th ACM international conference on hybrid systems: computation and control, HSCC 2010, Stockholm, Sweden, April 12--16, 2010. New York, NY: Association for Computing Machinery (ACM). 221--230 (2010; Zbl 1360.34082) Full Text: DOI
Zhu, Jiaofeng; Liu, Yinping Computer automated derivation of conservation laws for nonlinear differential-difference equations. (Chinese. English summary) Zbl 1240.34026 J. East China Norm. Univ., Nat. Sci. Ed. 2010, No. 1, 24-33 (2010). MSC: 34A33 34A05 34-04 68W30 PDFBibTeX XMLCite \textit{J. Zhu} and \textit{Y. Liu}, J. East China Norm. Univ., Nat. Sci. Ed. 2010, No. 1, 24--33 (2010; Zbl 1240.34026)
Irtegov, Valentin; Titorenko, Tatyana On reduction of Lagrange systems. (English) Zbl 1202.70074 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 12th international workshop, CASC 2010, Tsakhkadzor, Armenia, September 6–12, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15273-3/pbk). Lecture Notes in Computer Science 6244, 123-133 (2010). MSC: 70H33 68W30 PDFBibTeX XMLCite \textit{V. Irtegov} and \textit{T. Titorenko}, Lect. Notes Comput. Sci. 6244, 123--133 (2010; Zbl 1202.70074) Full Text: DOI
Cheviakov, Alexei F. Computation of fluxes of conservation laws. (English) Zbl 1193.65155 J. Eng. Math. 66, No. 1-3, 153-173 (2010). Reviewer: Qin Mengzhao (Beijing) MSC: 65M06 35L65 35B06 68W30 65-02 PDFBibTeX XMLCite \textit{A. F. Cheviakov}, J. Eng. Math. 66, No. 1--3, 153--173 (2010; Zbl 1193.65155) Full Text: DOI arXiv
Hereman, Willy; Adams, Paul J.; Eklund, Holly L.; Hickman, Mark S.; Herbst, Barend M. Direct methods and symbolic software for conservation laws of nonlinear equations. (English) Zbl 1210.35164 Yan, Zhenya (ed.), Advances in nonlinear waves and symbolic computation. New York, NY: Nova Science Publishers (ISBN 978-1-60692-260-6). 19-78 (2009). MSC: 35L65 34A33 68W30 35A30 35Q53 70S10 PDFBibTeX XMLCite \textit{W. Hereman} et al., in: Advances in nonlinear waves and symbolic computation. New York, NY: Nova Science Publishers. 19--78 (2009; Zbl 1210.35164) Full Text: arXiv
Yang, Xu-Dong; Ruan, Hang-Yu; Lou, Sen-Yue An extension of algorithm on symbolic computations of conserved densities for high-dimensional nonlinear systems. (English) Zbl 1392.68446 Commun. Theor. Phys. 50, No. 1, 23-30 (2008). MSC: 68W30 35-04 35B06 35Q53 PDFBibTeX XMLCite \textit{X.-D. Yang} et al., Commun. Theor. Phys. 50, No. 1, 23--30 (2008; Zbl 1392.68446) Full Text: DOI
Kari, Jarkko; Taati, Siamak Combinatorics of conservation laws. (English) Zbl 1169.68530 Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 95, 183-197 (2008). MSC: 68Q80 37B15 35L65 82C20 PDFBibTeX XMLCite \textit{J. Kari} and \textit{S. Taati}, Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 95, 183--197 (2008; Zbl 1169.68530)
Yang, Xu-Dong; Ruan, Hang-Yu; Lou, Sen-Yue A Maple package on symbolic computation of conserved densities for \((1+1)\)-dimensional nonlinear evolution systems. (English) Zbl 1355.68297 Commun. Theor. Phys. 47, No. 6, 961-968 (2007). MSC: 68W30 35L65 35Q53 35G20 PDFBibTeX XMLCite \textit{X.-D. Yang} et al., Commun. Theor. Phys. 47, No. 6, 961--968 (2007; Zbl 1355.68297) Full Text: DOI
Steeb, Willi-Hans Continuous symmetries, Lie algebras, differential equations, and computer algebra. 2nd ed. (English) Zbl 1159.35001 Singapore: World Scientific (ISBN 978-981-270-809-0/hbk). xiv, 457 p. (2007). Reviewer: Werner M. Seiler (Kassel) MSC: 35-01 22E60 22E70 35A30 35Q51 37K05 37K10 37K35 68W30 58J70 PDFBibTeX XMLCite \textit{W.-H. Steeb}, Continuous symmetries, Lie algebras, differential equations, and computer algebra. 2nd ed. Singapore: World Scientific (2007; Zbl 1159.35001)
Hannoun, Noureddine; Alexiades, Vasilios Issues in adaptive mesh refinement implementation. (English) Zbl 1113.65115 Electron. J. Differ. Equ. 2007, Conf. 15, 141-151 (2007). MSC: 65N50 65M50 65Y20 68N19 PDFBibTeX XMLCite \textit{N. Hannoun} and \textit{V. Alexiades}, Electron. J. Differ. Equ. 2007, 141--151 (2007; Zbl 1113.65115) Full Text: EuDML EMIS
Cervera, J.; Van der Schaft, A. J.; Baños, A. Interconnection of port-Hamiltonian systems and composition of Dirac structures. (English) Zbl 1115.93021 Automatica 43, No. 2, 212-225 (2007). MSC: 93B29 37K05 93B10 93C10 68M10 PDFBibTeX XMLCite \textit{J. Cervera} et al., Automatica 43, No. 2, 212--225 (2007; Zbl 1115.93021) Full Text: DOI Link
Hereman, Willy Symbolic computation of conservation laws of nonlinear partial differential equations in multi-dimensions. (English) Zbl 1188.68364 Int. J. Quantum Chem. 106, No. 1, 278-299 (2006). MSC: 68W30 35L65 PDFBibTeX XMLCite \textit{W. Hereman}, Int. J. Quantum Chem. 106, No. 1, 278--299 (2006; Zbl 1188.68364) Full Text: DOI arXiv
Niño-Mora, José Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue. (English) Zbl 1117.90035 Queueing Syst. 54, No. 4, 281-312 (2006). MSC: 90B22 90B36 90B18 60K25 60K30 68M20 PDFBibTeX XMLCite \textit{J. Niño-Mora}, Queueing Syst. 54, No. 4, 281--312 (2006; Zbl 1117.90035) Full Text: DOI Link
Yao, Ruo-Xia; Li, Zhi-Bin CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations. (English) Zbl 1090.65124 Appl. Math. Comput. 173, No. 1, 616-635 (2006). MSC: 65M70 65Y15 68W30 37K10 65P10 37M15 35L65 35Q53 PDFBibTeX XMLCite \textit{R.-X. Yao} and \textit{Z.-B. Li}, Appl. Math. Comput. 173, No. 1, 616--635 (2006; Zbl 1090.65124) Full Text: DOI
Yao, Ruoxia; Li, Zhibin CONSLAW: a Maple package to construct the conservation laws for nonlinear evolution equations. (English) Zbl 1108.35030 Wang, Dongming (ed.) et al., Differential equations with symbolic computation. Basel: Birkhäuser (ISBN 3-7643-7368-7/hbk). Trends in Mathematics, 307-325 (2005). Reviewer: Werner M. Seiler (Kassel) MSC: 35G25 35Q53 37K05 68W30 PDFBibTeX XMLCite \textit{R. Yao} and \textit{Z. Li}, in: Differential equations with symbolic computation. Basel: Birkhäuser. 307--325 (2005; Zbl 1108.35030)
Gouveia, Paulo D. F.; Torres, Delfim F. M. Automatic computation of conservation laws in the calculus of variations and optimal control. (English) Zbl 1079.49019 Comput. Methods Appl. Math. 5, No. 4, 387-409 (2005). MSC: 49K15 49-04 49S05 68W30 PDFBibTeX XMLCite \textit{P. D. F. Gouveia} and \textit{D. F. M. Torres}, Comput. Methods Appl. Math. 5, No. 4, 387--409 (2005; Zbl 1079.49019) Full Text: DOI arXiv
Hereman, W.; Sanders, J. A.; Sayers, J.; Wang, J. P. Symbolic computation of polynomial conserved densities, generalized symmetries, and recursion operators for nonlinear differential-difference equations. (English) Zbl 1080.65119 Winternitz, P. (ed.) et al., Group theory and numerical analysis. Selected papers based on the presentation at the workshop, Montréal, Canada, May 26–31, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3565-3/pbk). CRM Proceedings and Lecture Notes 39, 133-148 (2005). MSC: 65P10 35Q58 37J35 37K05 68W30 37K10 37M15 34K28 PDFBibTeX XMLCite \textit{W. Hereman} et al., in: Group theory and numerical analysis. Selected papers based on the presentation at the workshop, Montréal, Canada, May 26--31, 2003. Providence, RI: American Mathematical Society (AMS). 133--148 (2005; Zbl 1080.65119) Full Text: arXiv
Baldwin, D.; Hereman, W.; Sayers, J. Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs. (English) Zbl 1080.65094 Winternitz, P. (ed.) et al., Group theory and numerical analysis. Selected papers based on the presentation at the workshop, Montréal, Canada, May 26–31, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3565-3/pbk). CRM Proceedings and Lecture Notes 39, 17-32 (2005). MSC: 65M70 35Q53 65Y15 68W30 37K10 37K40 37K05 PDFBibTeX XMLCite \textit{D. Baldwin} et al., in: Group theory and numerical analysis. Selected papers based on the presentation at the workshop, Montréal, Canada, May 26--31, 2003. Providence, RI: American Mathematical Society (AMS). 17--32 (2005; Zbl 1080.65094) Full Text: arXiv
Kari, Jarkko Theory of cellular automata: a survey. (English) Zbl 1080.68070 Theor. Comput. Sci. 334, No. 1-3, 3-33 (2005). MSC: 68Q80 37B15 68-02 37-02 PDFBibTeX XMLCite \textit{J. Kari}, Theor. Comput. Sci. 334, No. 1--3, 3--33 (2005; Zbl 1080.68070) Full Text: DOI
Katzenelson, Jacob Notes on amorphous computing. (English) Zbl 1045.65075 Int. J. Pure Appl. Math. 6, No. 2, 145-184 (2003). MSC: 65M06 35L65 65M12 35Q60 65Y10 68M14 PDFBibTeX XMLCite \textit{J. Katzenelson}, Int. J. Pure Appl. Math. 6, No. 2, 145--184 (2003; Zbl 1045.65075)
Wolf, Thomas The integration of systems of linear PDEs using conservation laws of syzygies. (English) Zbl 1026.35003 J. Symb. Comput. 35, No. 5, 499-526 (2003). Reviewer: Valery A.Yumaguzhin (Pereslavl’-Zalesskij) MSC: 35A25 65K05 35N10 35A30 35L65 68W30 PDFBibTeX XMLCite \textit{T. Wolf}, J. Symb. Comput. 35, No. 5, 499--526 (2003; Zbl 1026.35003) Full Text: DOI
Pivato, Marcus Conservation laws in cellular automata. (English) Zbl 1013.37008 Nonlinearity 15, No. 6, 1781-1793 (2002). Reviewer: Thomas Ward (Norwich) MSC: 37B15 68Q80 PDFBibTeX XMLCite \textit{M. Pivato}, Nonlinearity 15, No. 6, 1781--1793 (2002; Zbl 1013.37008) Full Text: DOI arXiv
Arandiga, F.; Chiavassa, G.; Donat, R. Applications of Harten’s framework for multiresolution: From conservation laws to image compression. (With color plate 7). (English) Zbl 0992.65153 Barth, Timothy J. (ed.) et al., Multiscale and multiresolution methods. Theory and applications. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 20, 281-296, 386 (2002). MSC: 65T60 35L65 42C40 65M60 68U10 PDFBibTeX XMLCite \textit{F. Arandiga} et al., Lect. Notes Comput. Sci. Eng. 20, 281--296, 386 (2002; Zbl 0992.65153)
Prytula, Mykola; Vorobjova, O. Application of computer algebra methods in investigating the integrability of the nonlinear dynamical systems on functional manifolds. (Ukrainian. English summary) Zbl 0972.35129 Visn. L’viv. Univ., Ser. Prykl. Mat. Inform. 2000, No. 2, 67-71 (2000). MSC: 35Q53 35-04 68U01 37K05 PDFBibTeX XMLCite \textit{M. Prytula} and \textit{O. Vorobjova}, Visn. L'viv. Univ., Ser. Prykl. Mat. Inform. 2000, No. 2, 67--71 (2000; Zbl 0972.35129)
Wolf, Thomas The symbolic integration of exact PDEs. (English) Zbl 1054.68171 J. Symb. Comput. 30, No. 5, 619-629 (2000). MSC: 68W30 35F20 35L65 PDFBibTeX XMLCite \textit{T. Wolf}, J. Symb. Comput. 30, No. 5, 619--629 (2000; Zbl 1054.68171) Full Text: DOI
Kiselev, S. P.; Vorozhtsov, E. V.; Fomin, V. M. Foundations of fluid mechanics with applications. Problem solving using Mathematica. (English) Zbl 0937.76001 Boston: Birkhäuser (ISBN 0-8176-3995-0). xiv, 575 p. (1999). Reviewer: Thomas Sonar (Braunschweig) MSC: 76-02 76Mxx 68W30 PDFBibTeX XMLCite \textit{S. P. Kiselev} et al., Foundations of fluid mechanics with applications. Problem solving using \textit{Mathematica}. Boston: Birkhäuser (1999; Zbl 0937.76001)
Wilkins, Mark L. Computer simulation of dynamic phenomena. (English) Zbl 0926.76001 Scientific Computation. Berlin: Springer. xvi, 246 p. (1999). Reviewer: A.I.Tolstykh (Moskva) MSC: 76-02 74-02 68U20 76M20 74S20 PDFBibTeX XMLCite \textit{M. L. Wilkins}, Computer simulation of dynamic phenomena. Berlin: Springer (1999; Zbl 0926.76001)
Wolf, Thomas; Brand, Andreas; Mohammadzadeh, Majid Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions. (English) Zbl 0919.65076 J. Symb. Comput. 27, No. 2, 221-238 (1999). Reviewer: P.K.Mahanti (Ranchi) MSC: 65Z05 65Y15 35L65 35-04 68W30 PDFBibTeX XMLCite \textit{T. Wolf} et al., J. Symb. Comput. 27, No. 2, 221--238 (1999; Zbl 0919.65076) Full Text: DOI Link
Tóth, Gábor The LASY preprocessor and its application to general multidimensional codes. (English) Zbl 0903.76077 J. Comput. Phys. 138, No. 2, 981-990 (1997). MSC: 76M99 68N15 PDFBibTeX XMLCite \textit{G. Tóth}, J. Comput. Phys. 138, No. 2, 981--990 (1997; Zbl 0903.76077) Full Text: DOI Link
Göktaş, Ünal; Hereman, Willy Symbolic computations of conserved densities for systems of nonlinear evolution equations. (English) Zbl 0891.65129 J. Symb. Comput. 24, No. 5, 591-621 (1997). MSC: 65Z05 35Q51 65Y15 35Q53 68W30 PDFBibTeX XMLCite \textit{Ü. Göktaş} and \textit{W. Hereman}, J. Symb. Comput. 24, No. 5, 591--621 (1997; Zbl 0891.65129) Full Text: DOI arXiv
Baumann, G. Symmetry analysis of differential equations with MATHEMATICA. (English) Zbl 0898.34003 Math. Comput. Modelling 25, No. 8-9, 25-37 (1997). Reviewer: K.Gatermann (Berlin) MSC: 34-04 68Q25 34L40 35Q55 22E99 35L65 PDFBibTeX XMLCite \textit{G. Baumann}, Math. Comput. Modelling 25, No. 8--9, 25--37 (1997; Zbl 0898.34003) Full Text: DOI