Mittal, A. K. A space-time pseudospectral method for solving multi-dimensional quasi-linear parabolic partial differential (Burgers’) equations. (English) Zbl 07763847 Appl. Numer. Math. 195, 39-53 (2024). MSC: 65Mxx 35Qxx 65Nxx PDFBibTeX XMLCite \textit{A. K. Mittal}, Appl. Numer. Math. 195, 39--53 (2024; Zbl 07763847) Full Text: DOI
Abbaszadeh, Mostafa; Zaky, Mahmoud A.; Hendy, Ahmed S.; Dehghan, Mehdi A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers’ equation. (English) Zbl 07705774 Appl. Numer. Math. 187, 262-276 (2023). MSC: 65Mxx 65Nxx 35Qxx PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., Appl. Numer. Math. 187, 262--276 (2023; Zbl 07705774) Full Text: DOI
Zara, Aiman; Rehman, Shafiq Ur; Ahmad, Fayyaz Kernel smoothing method for the numerical approximation of Benjamin-Bona-Mahony-Burgers’ equation. (English) Zbl 07699044 Appl. Numer. Math. 186, 320-333 (2023). MSC: 65Mxx 35Qxx 65-XX PDFBibTeX XMLCite \textit{A. Zara} et al., Appl. Numer. Math. 186, 320--333 (2023; Zbl 07699044) Full Text: DOI
Xu, Chao; Pei, Lifang Unconditional superconvergence analysis of two modified finite element fully discrete schemes for nonlinear Burgers’ equation. (English) Zbl 07698995 Appl. Numer. Math. 185, 1-17 (2023). MSC: 65Mxx 65Nxx 76Mxx PDFBibTeX XMLCite \textit{C. Xu} and \textit{L. Pei}, Appl. Numer. Math. 185, 1--17 (2023; Zbl 07698995) Full Text: DOI
Tahir, Shko Ali; Sari, Murat A new approach for the coupled advection-diffusion processes including source effects. (English) Zbl 1507.65146 Appl. Numer. Math. 184, 391-405 (2023). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65D07 65L05 65H10 65F05 41A15 35Q53 PDFBibTeX XMLCite \textit{S. A. Tahir} and \textit{M. Sari}, Appl. Numer. Math. 184, 391--405 (2023; Zbl 1507.65146) Full Text: DOI
Azarnavid, Babak; Emamjomeh, Mahdi; Nabati, Mohammad An efficient kernel-based method for solving nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in irregular domains. (English) Zbl 1502.65157 Appl. Numer. Math. 181, 518-533 (2022). MSC: 65M70 65M12 35Q53 PDFBibTeX XMLCite \textit{B. Azarnavid} et al., Appl. Numer. Math. 181, 518--533 (2022; Zbl 1502.65157) Full Text: DOI
Pan, Yueyue; Wu, Lifei; Yang, Xiaozhong A difference method with intrinsic parallelism for the variable-coefficient compound KdV-Burgers equation. (English) Zbl 1486.65124 Appl. Numer. Math. 169, 201-220 (2021). MSC: 65M06 65M12 65Y05 35Q53 PDFBibTeX XMLCite \textit{Y. Pan} et al., Appl. Numer. Math. 169, 201--220 (2021; Zbl 1486.65124) Full Text: DOI
Chen, Li; Lü, Shujuan; Xu, Tao Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions. (English) Zbl 1486.65190 Appl. Numer. Math. 169, 164-178 (2021). MSC: 65M70 65M06 65N35 65M12 65M15 26A33 35B65 35R11 35Q53 PDFBibTeX XMLCite \textit{L. Chen} et al., Appl. Numer. Math. 169, 164--178 (2021; Zbl 1486.65190) Full Text: DOI
Verma, Amit Kumar; Rawani, Mukesh Kumar; Cattani, Carlo A numerical scheme for a class of generalized Burgers’ equation based on Haar wavelet nonstandard finite difference method. (English) Zbl 1486.65211 Appl. Numer. Math. 168, 41-54 (2021). MSC: 65M70 65T60 65M06 65M15 35Q53 PDFBibTeX XMLCite \textit{A. K. Verma} et al., Appl. Numer. Math. 168, 41--54 (2021; Zbl 1486.65211) Full Text: DOI
Yang, Huaijun Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers’ type nonlinearity. (English) Zbl 1478.65092 Appl. Numer. Math. 168, 13-22 (2021). MSC: 65M60 65M06 65N30 65M12 65M15 76S05 35Q35 PDFBibTeX XMLCite \textit{H. Yang}, Appl. Numer. Math. 168, 13--22 (2021; Zbl 1478.65092) Full Text: DOI
Destuynder, Philippe; Liberge, Erwan A few remarks on penalty and penalty-duality methods in fluid-structure interactions. (English) Zbl 1466.76019 Appl. Numer. Math. 167, 1-30 (2021). MSC: 76D55 76M30 74F10 PDFBibTeX XMLCite \textit{P. Destuynder} and \textit{E. Liberge}, Appl. Numer. Math. 167, 1--30 (2021; Zbl 1466.76019) Full Text: DOI arXiv
Khan, Feroz Higher order pathwise approximation for the stochastic Burgers’ equation with additive noise. (English) Zbl 1468.60080 Appl. Numer. Math. 162, 67-80 (2021). MSC: 60H15 65C30 60H35 35Q53 PDFBibTeX XMLCite \textit{F. Khan}, Appl. Numer. Math. 162, 67--80 (2021; Zbl 1468.60080) Full Text: DOI
Arora, Shelly; Jain, Rajiv; Kukreja, V. K. Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines. (English) Zbl 1437.65164 Appl. Numer. Math. 154, 1-16 (2020). MSC: 65N08 65M06 65M12 65D07 35Q53 PDFBibTeX XMLCite \textit{S. Arora} et al., Appl. Numer. Math. 154, 1--16 (2020; Zbl 1437.65164) Full Text: DOI
Hosseini, Rasool; Tatari, Mehdi Some splitting methods for hyperbolic PDEs. (English) Zbl 1459.65143 Appl. Numer. Math. 146, 361-378 (2019). MSC: 65M06 35B50 35Q53 PDFBibTeX XMLCite \textit{R. Hosseini} and \textit{M. Tatari}, Appl. Numer. Math. 146, 361--378 (2019; Zbl 1459.65143) Full Text: DOI
Cook, Stephen; Budd, Chris; Hill, Adrian; Melvin, Thomas Error estimates for semi-Lagrangian finite difference methods applied to Burgers’ equation in one dimension. (English) Zbl 1433.65188 Appl. Numer. Math. 145, 261-282 (2019). Reviewer: Yajuan Sun (Beijing) MSC: 65M20 65M15 35Q53 86A10 65M06 PDFBibTeX XMLCite \textit{S. Cook} et al., Appl. Numer. Math. 145, 261--282 (2019; Zbl 1433.65188) Full Text: DOI
Zheng, Quan; Zhao, Xin; Liu, Yufeng A novel finite difference scheme for Burgers’ equation on unbounded domains. (English) Zbl 1353.65092 Appl. Numer. Math. 111, 1-16 (2017). MSC: 65M06 65M12 65M15 35Q53 PDFBibTeX XMLCite \textit{Q. Zheng} et al., Appl. Numer. Math. 111, 1--16 (2017; Zbl 1353.65092) Full Text: DOI
Towers, John D. A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. (English) Zbl 06638248 Appl. Numer. Math. 110, 26-40 (2016). MSC: 65-XX PDFBibTeX XMLCite \textit{J. D. Towers}, Appl. Numer. Math. 110, 26--40 (2016; Zbl 06638248) Full Text: DOI
Tiago, Jorge Numerical simulations for the stabilization and estimation problem of a semilinear partial differential equation. (English) Zbl 1329.65230 Appl. Numer. Math. 98, 18-37 (2015). MSC: 65M60 35K20 35K59 65M12 35Q53 PDFBibTeX XMLCite \textit{J. Tiago}, Appl. Numer. Math. 98, 18--37 (2015; Zbl 1329.65230) Full Text: DOI
Liu, Yaning; Hussaini, M. Yousuff; Ökten, Giray Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives. (English) Zbl 1302.65013 Appl. Numer. Math. 72, 160-171 (2013). MSC: 65C05 35Q53 PDFBibTeX XMLCite \textit{Y. Liu} et al., Appl. Numer. Math. 72, 160--171 (2013; Zbl 1302.65013) Full Text: DOI
Bouhamidi, A.; Hached, M.; Jbilou, K. A meshless method for the numerical computation of the solution of steady Burgers-type equations. (English) Zbl 1302.65259 Appl. Numer. Math. 74, 95-110 (2013). MSC: 65N35 65N22 65F10 PDFBibTeX XMLCite \textit{A. Bouhamidi} et al., Appl. Numer. Math. 74, 95--110 (2013; Zbl 1302.65259) Full Text: DOI
Jordan, Stephen A. Optimization, resolution and application of composite compact finite difference templates. (English) Zbl 1204.65104 Appl. Numer. Math. 61, No. 1, 108-130 (2011). MSC: 65M06 65M12 65M15 35L45 35Q53 PDFBibTeX XMLCite \textit{S. A. Jordan}, Appl. Numer. Math. 61, No. 1, 108--130 (2011; Zbl 1204.65104) Full Text: DOI
Wang, Jin; Layton, Anita New numerical methods for Burgers’ equation based on semi-Lagrangian and modified equation approaches. (English) Zbl 1191.65115 Appl. Numer. Math. 60, No. 6, 645-657 (2010). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{J. Wang} and \textit{A. Layton}, Appl. Numer. Math. 60, No. 6, 645--657 (2010; Zbl 1191.65115) Full Text: DOI
Luo, Zhendong; Zhou, Yanjie; Yang, Xiaozhong A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation. (English) Zbl 1169.65096 Appl. Numer. Math. 59, No. 8, 1933-1946 (2009). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65M60 35Q53 65M15 PDFBibTeX XMLCite \textit{Z. Luo} et al., Appl. Numer. Math. 59, No. 8, 1933--1946 (2009; Zbl 1169.65096) Full Text: DOI
Huang, Chengming Strong stability preserving hybrid methods. (English) Zbl 1163.65063 Appl. Numer. Math. 59, No. 5, 891-904 (2009). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65M12 65M20 35L70 PDFBibTeX XMLCite \textit{C. Huang}, Appl. Numer. Math. 59, No. 5, 891--904 (2009; Zbl 1163.65063) Full Text: DOI
Peer, A. A. I.; Gopaul, A.; Dauhoo, M. Z.; Bhuruth, M. A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws. (English) Zbl 1138.65075 Appl. Numer. Math. 58, No. 5, 674-688 (2008). MSC: 65M06 35L65 35Q53 PDFBibTeX XMLCite \textit{A. A. I. Peer} et al., Appl. Numer. Math. 58, No. 5, 674--688 (2008; Zbl 1138.65075) Full Text: DOI
Shen, Jie; Wang, Li-Lian Fourierization of the Legendre-Galerkin method and a new space-time spectral method. (English) Zbl 1118.65111 Appl. Numer. Math. 57, No. 5-7, 710-720 (2007). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M70 65M15 65M12 65M20 35K55 35Q53 35Q55 PDFBibTeX XMLCite \textit{J. Shen} and \textit{L.-L. Wang}, Appl. Numer. Math. 57, No. 5--7, 710--720 (2007; Zbl 1118.65111) Full Text: DOI
Pantano, C. An additive semi-implicit Runge–Kutta family of schemes for nonstiff systems. (English) Zbl 1107.65331 Appl. Numer. Math. 57, No. 3, 297-303 (2007). MSC: 65L06 65L05 34A34 65L20 65M20 35Q53 PDFBibTeX XMLCite \textit{C. Pantano}, Appl. Numer. Math. 57, No. 3, 297--303 (2007; Zbl 1107.65331) Full Text: DOI
Svärd, Magnus; Gong, Jing; Nordström, Jan Stable artificial dissipation operators for finite volume schemes on unstructured grids. (English) Zbl 1103.65096 Appl. Numer. Math. 56, No. 12, 1481-1490 (2006). MSC: 65M06 65M12 35K05 35L45 35Q53 PDFBibTeX XMLCite \textit{M. Svärd} et al., Appl. Numer. Math. 56, No. 12, 1481--1490 (2006; Zbl 1103.65096) Full Text: DOI Link
Cao, Yanzhao; Hussaini, M. Y.; Zang, T.; Zatezalo, A. A variance reduction method based on sensitivity derivatives. (English) Zbl 1098.65003 Appl. Numer. Math. 56, No. 6, 800-813 (2006). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 65C05 60H15 60H35 35Q53 PDFBibTeX XMLCite \textit{Y. Cao} et al., Appl. Numer. Math. 56, No. 6, 800--813 (2006; Zbl 1098.65003) Full Text: DOI
Morandi Cecchi, Maria; Pirozzi, Maria Antonietta High order finite difference numerical methods for time-dependent convection-dominated problems. (English) Zbl 1083.65078 Appl. Numer. Math. 55, No. 3, 334-356 (2005). Reviewer: Roland Pulch (Wuppertal) MSC: 65M06 65M12 35L65 65M15 PDFBibTeX XMLCite \textit{M. Morandi Cecchi} and \textit{M. A. Pirozzi}, Appl. Numer. Math. 55, No. 3, 334--356 (2005; Zbl 1083.65078) Full Text: DOI
Sarra, Scott A. Adaptive radial basis function methods for time dependent partial differential equations. (English) Zbl 1069.65109 Appl. Numer. Math. 54, No. 1, 79-94 (2005). MSC: 65M70 PDFBibTeX XMLCite \textit{S. A. Sarra}, Appl. Numer. Math. 54, No. 1, 79--94 (2005; Zbl 1069.65109) Full Text: DOI
Berzins, M. Variable-order finite elements and positivity preservation for hyperbolic PDEs. (English) Zbl 1038.65093 Appl. Numer. Math. 48, No. 3-4, 271-292 (2004). MSC: 65M60 35L45 35Q53 PDFBibTeX XMLCite \textit{M. Berzins}, Appl. Numer. Math. 48, No. 3--4, 271--292 (2004; Zbl 1038.65093) Full Text: DOI
Calvo, M. P.; de Frutos, J.; Novo, J. Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations. (English) Zbl 0983.65106 Appl. Numer. Math. 37, No. 4, 535-549 (2001). MSC: 65M20 65M12 35K15 35Q53 65L06 PDFBibTeX XMLCite \textit{M. P. Calvo} et al., Appl. Numer. Math. 37, No. 4, 535--549 (2001; Zbl 0983.65106) Full Text: DOI
Roberts, A. J. Holistic discretization ensures fidelity to Burgers’ equation. (English) Zbl 0984.65090 Appl. Numer. Math. 37, No. 3, 371-396 (2001). Reviewer: J.D.P.Donnelly (Oxford) MSC: 65M06 65M12 35Q53 PDFBibTeX XMLCite \textit{A. J. Roberts}, Appl. Numer. Math. 37, No. 3, 371--396 (2001; Zbl 0984.65090) Full Text: DOI
Chiavassa, G.; Liandrat, J. A fully adaptive wavelet algorithm for parabolic partial differential equations. (English) Zbl 0973.65089 Appl. Numer. Math. 36, No. 2-3, 333-358 (2001). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 65M70 35K05 35Q53 65T60 PDFBibTeX XMLCite \textit{G. Chiavassa} and \textit{J. Liandrat}, Appl. Numer. Math. 36, No. 2--3, 333--358 (2001; Zbl 0973.65089) Full Text: DOI
Black, Kelly Spectral element approximation of convection-diffusion type problems. (English) Zbl 0964.65104 Appl. Numer. Math. 33, No. 1-4, 373-379 (2000). MSC: 65M60 35K05 35Q53 65M70 PDFBibTeX XMLCite \textit{K. Black}, Appl. Numer. Math. 33, No. 1--4, 373--379 (2000; Zbl 0964.65104) Full Text: DOI
Gelb, Anne; Tadmor, Eitan Enhanced spectral viscosity approximations for conservation laws. (English) Zbl 0973.65088 Appl. Numer. Math. 33, No. 1-4, 3-21 (2000). Reviewer: S.Benzoni (Lyon) MSC: 65M70 35L65 PDFBibTeX XMLCite \textit{A. Gelb} and \textit{E. Tadmor}, Appl. Numer. Math. 33, No. 1--4, 3--21 (2000; Zbl 0973.65088) Full Text: DOI
Efraimsson, Gunilla; Kreiss, Gunilla A note on the effect of artificial viscosity on solutions of conservation laws. (English) Zbl 0860.65079 Appl. Numer. Math. 21, No. 2, 155-173 (1996). Reviewer: S.Migorski (Krakow) MSC: 65M06 35L65 76N15 PDFBibTeX XMLCite \textit{G. Efraimsson} and \textit{G. Kreiss}, Appl. Numer. Math. 21, No. 2, 155--173 (1996; Zbl 0860.65079) Full Text: DOI
Crossley, P. S.; Saunders, R.; Causon, D. M.; Mingham, C. G. A spectral method with subcell resolution for shock wave calculations. (English) Zbl 0866.65065 Appl. Numer. Math. 21, No. 2, 141-153 (1996). Reviewer: N.Vulchanov (Sofia) MSC: 65M70 35L67 76N15 35Q53 PDFBibTeX XMLCite \textit{P. S. Crossley} et al., Appl. Numer. Math. 21, No. 2, 141--153 (1996; Zbl 0866.65065) Full Text: DOI
Devine, Karen D.; Flaherty, Joseph E. Parallel adaptive \(hp\)-refinement techniques for conservation laws. (English) Zbl 0860.65095 Appl. Numer. Math. 20, No. 4, 367-386 (1996). Reviewer: V.P.Tyagi (Bombay) MSC: 65M60 65M50 35L65 76N15 35Q53 PDFBibTeX XMLCite \textit{K. D. Devine} and \textit{J. E. Flaherty}, Appl. Numer. Math. 20, No. 4, 367--386 (1996; Zbl 0860.65095) Full Text: DOI
Huang, Weizhang; Russell, Robert D. A moving collocation method for solving time dependent partial differential equations. (English) Zbl 0859.65112 Appl. Numer. Math. 20, No. 1-2, 101-116 (1996). Reviewer: A.I.Tolstykh (Moskva) MSC: 65M70 65M06 65M50 35L70 35Q53 PDFBibTeX XMLCite \textit{W. Huang} and \textit{R. D. Russell}, Appl. Numer. Math. 20, No. 1--2, 101--116 (1996; Zbl 0859.65112) Full Text: DOI
Garcia, Salvador Higher-order incremental unknowns, hiearchical basis, and nonlinear dissipative evolutionary equations. (English) Zbl 0857.65086 Appl. Numer. Math. 19, No. 4, 467-494 (1996). Reviewer: E.Schechter (Kaiserslautern) MSC: 65M06 35Q53 35K55 PDFBibTeX XMLCite \textit{S. Garcia}, Appl. Numer. Math. 19, No. 4, 467--494 (1996; Zbl 0857.65086) Full Text: DOI
Laminie, Jacques; Pascal, Frédéric; Temam, Roger Implementation and numerical analysis of the nonlinear Galerkin methods with finite elements discretization. (English) Zbl 0816.65064 Appl. Numer. Math. 15, No. 2, 219-246 (1994). Reviewer: P.Burda (Praha) MSC: 65M60 35Q53 35Q30 PDFBibTeX XMLCite \textit{J. Laminie} et al., Appl. Numer. Math. 15, No. 2, 219--246 (1994; Zbl 0816.65064) Full Text: DOI EuDML
Gottlieb, David; Temam, Roger Implementation of the nonlinear Galerkin method with pseudospectral (collocation) discretizations. (English) Zbl 0782.65122 Appl. Numer. Math. 12, No. 1-3, 119-134 (1993). Reviewer: K.Finck von Finckenstein (Darmstadt) MSC: 65M60 65M70 35K05 35Q53 PDFBibTeX XMLCite \textit{D. Gottlieb} and \textit{R. Temam}, Appl. Numer. Math. 12, No. 1--3, 119--134 (1993; Zbl 0782.65122) Full Text: DOI
Bona, Jerry L.; Dougalis, Vassilios A.; Karakashian, Ohannes A.; McKinney, William R. Computations of blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation. (English) Zbl 0757.65123 Appl. Numer. Math. 10, No. 3-4, 335-355 (1992). Reviewer: C.I.Gheorghiu (Cluj-Napoca) MSC: 65Z05 35Q53 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Appl. Numer. Math. 10, No. 3--4, 335--355 (1992; Zbl 0757.65123) Full Text: DOI
Hyman, James M.; Larrouturou, Bernard Dynamic rezone methods for partial differential equations in one space dimension. (English) Zbl 0678.65085 Appl. Numer. Math. 5, No. 5, 435-450 (1989). Reviewer: V.P.Tyagi MSC: 65Z05 65N50 65N15 35Q99 PDFBibTeX XMLCite \textit{J. M. Hyman} and \textit{B. Larrouturou}, Appl. Numer. Math. 5, No. 5, 435--450 (1989; Zbl 0678.65085) Full Text: DOI
Kreiss, Gunilla; Kreiss, Heinz-Otto Convergence to steady state of solutions of Burgers’ equation. (English) Zbl 0631.65121 Appl. Numer. Math. 2, 161-179 (1986). Reviewer: V.P.Tyagi MSC: 65Z05 65N12 35Q99 76N15 PDFBibTeX XMLCite \textit{G. Kreiss} and \textit{H.-O. Kreiss}, Appl. Numer. Math. 2, 161--179 (1986; Zbl 0631.65121) Full Text: DOI Link