Murray, Maxime; Mireles James, J. D. Computer assisted proof of homoclinic chaos in the spatial equilateral restricted four-body problem. (English) Zbl 07765633 J. Differ. Equations 378, 559-609 (2024). MSC: 70F10 70K55 70K44 70H12 70-08 PDFBibTeX XMLCite \textit{M. Murray} and \textit{J. D. Mireles James}, J. Differ. Equations 378, 559--609 (2024; Zbl 07765633) Full Text: DOI arXiv
Liao, Xian; Plum, Michael Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schrödinger equation. (English) Zbl 07764511 SIAM J. Math. Anal. 55, No. 6, 7399-7425 (2023). Reviewer: Xiaoming He (Beijing) MSC: 35Q55 37K10 35B53 35P30 PDFBibTeX XMLCite \textit{X. Liao} and \textit{M. Plum}, SIAM J. Math. Anal. 55, No. 6, 7399--7425 (2023; Zbl 07764511) Full Text: DOI arXiv
Hur, Vera Mikyoung; Yang, Zhao Unstable Stokes waves. (English) Zbl 1521.35139 Arch. Ration. Mech. Anal. 247, No. 4, Paper No. 62, 59 p. (2023). MSC: 35Q35 76B15 76D07 35B35 35P99 PDFBibTeX XMLCite \textit{V. M. Hur} and \textit{Z. Yang}, Arch. Ration. Mech. Anal. 247, No. 4, Paper No. 62, 59 p. (2023; Zbl 1521.35139) Full Text: DOI arXiv
Allen, Mark; Barker, Blake; Gardiner, Jason; Zhao, Mingyan Minimizers of a free boundary problem on three-dimensional cones. (English) Zbl 1501.35461 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 226, Article ID 113152, 14 p. (2023). MSC: 35R35 35J20 35J65 PDFBibTeX XMLCite \textit{M. Allen} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 226, Article ID 113152, 14 p. (2023; Zbl 1501.35461) Full Text: DOI arXiv
Takayasu, Akitoshi; Lessard, Jean-Philippe; Jaquette, Jonathan; Okamoto, Hisashi Rigorous numerics for nonlinear heat equations in the complex plane of time. (English) Zbl 07549404 Numer. Math. 151, No. 3, 693-750 (2022). MSC: 65-XX 35A20 35B40 35B44 35K55 65G40 65M15 65M70 PDFBibTeX XMLCite \textit{A. Takayasu} et al., Numer. Math. 151, No. 3, 693--750 (2022; Zbl 07549404) Full Text: DOI arXiv
Jaquette, Jonathan; Lessard, Jean-Philippe; Takayasu, Akitoshi Global dynamics in nonconservative nonlinear Schrödinger equations. (English) Zbl 1492.35309 Adv. Math. 398, Article ID 108234, 70 p. (2022). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35B40 35B20 37K99 37M21 35A01 PDFBibTeX XMLCite \textit{J. Jaquette} et al., Adv. Math. 398, Article ID 108234, 70 p. (2022; Zbl 1492.35309) Full Text: DOI arXiv
Jaquette, Jonathan; Lessard, Jean-Philippe; Takayasu, Akitoshi Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity. (English) Zbl 1483.35119 Commun. Nonlinear Sci. Numer. Simul. 107, Article ID 106188, 14 p. (2022). MSC: 35K58 35K20 35B44 37C29 PDFBibTeX XMLCite \textit{J. Jaquette} et al., Commun. Nonlinear Sci. Numer. Simul. 107, Article ID 106188, 14 p. (2022; Zbl 1483.35119) Full Text: DOI arXiv
Constantineau, Kevin; García-Azpeitia, Carlos; Lessard, Jean-Philippe Spatial relative equilibria and periodic solutions of the Coulomb \((n+1)\)-body problem. (English) Zbl 1493.70056 Qual. Theory Dyn. Syst. 21, No. 1, Paper No. 3, 19 p. (2022). MSC: 70F10 65G40 47H11 34C25 37G40 PDFBibTeX XMLCite \textit{K. Constantineau} et al., Qual. Theory Dyn. Syst. 21, No. 1, Paper No. 3, 19 p. (2022; Zbl 1493.70056) Full Text: DOI arXiv
van den Berg, Jan Bouwe; Sheombarsing, Ray Rigorous numerics for ODEs using Chebyshev series and domain decomposition. (English) Zbl 1481.65115 J. Comput. Dyn. 8, No. 3, 353-401 (2021). MSC: 65L99 34B15 PDFBibTeX XMLCite \textit{J. B. van den Berg} and \textit{R. Sheombarsing}, J. Comput. Dyn. 8, No. 3, 353--401 (2021; Zbl 1481.65115) Full Text: DOI
García-Azpeitia, Carlos; Lessard, Jean-Philippe Free vibrations in a wave equation modeling MEMS. (English) Zbl 1477.35014 SIAM J. Appl. Dyn. Syst. 19, No. 4, 2749-2782 (2020). Reviewer: Alois Steindl (Wien) MSC: 35B10 35B32 37M20 37N15 74H45 35L72 35L20 PDFBibTeX XMLCite \textit{C. García-Azpeitia} and \textit{J.-P. Lessard}, SIAM J. Appl. Dyn. Syst. 19, No. 4, 2749--2782 (2020; Zbl 1477.35014) Full Text: DOI arXiv
Takayasu, Akitoshi A computer-assisted proof for nonlinear heat equations in the complex plane of time. (English) Zbl 1455.35002 RIMS Kôkyûroku Bessatsu B82, 47-66 (2020). MSC: 35A20 35B40 35B44 35K55 65G40 65M15 65M70 PDFBibTeX XMLCite \textit{A. Takayasu}, RIMS Kôkyûroku Bessatsu B82, 47--66 (2020; Zbl 1455.35002) Full Text: Link
Hashimoto, Kouji; Kinoshita, Takehiko; Nakao, Mitsuhiro T. Numerical verification of solutions for nonlinear parabolic problems. (English) Zbl 1450.65121 Numer. Funct. Anal. Optim. 41, No. 12, 1495-1514 (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65M60 65M15 35K55 35K05 PDFBibTeX XMLCite \textit{K. Hashimoto} et al., Numer. Funct. Anal. Optim. 41, No. 12, 1495--1514 (2020; Zbl 1450.65121) Full Text: DOI arXiv
Zhao, Jisong; Li, Shuang Adaptive mesh refinement method for solving optimal control problems using interpolation error analysis and improved data compression. (English) Zbl 1448.49037 J. Franklin Inst. 357, No. 3, 1603-1627 (2020). Reviewer: Kamal Mamehrashi (Boukan) MSC: 49M25 90C30 65M50 PDFBibTeX XMLCite \textit{J. Zhao} and \textit{S. Li}, J. Franklin Inst. 357, No. 3, 1603--1627 (2020; Zbl 1448.49037) Full Text: DOI
Bánhelyi, Balázs; Csendes, Tibor; Hatvani, László On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum. (English) Zbl 1447.34042 J. Comput. Appl. Math. 371, Article ID 112702, 9 p. (2020). Reviewer: Oleg Anashkin (Simferopol) MSC: 34C25 34C15 34D20 34H15 70K40 34C28 34H10 PDFBibTeX XMLCite \textit{B. Bánhelyi} et al., J. Comput. Appl. Math. 371, Article ID 112702, 9 p. (2020; Zbl 1447.34042) Full Text: DOI Link
Bünger, Florian A Taylor model toolbox for solving ODEs implemented in Matlab/INTLAB. (English) Zbl 1429.65144 J. Comput. Appl. Math. 368, Article ID 112511, 20 p. (2020). MSC: 65L05 34-04 34A34 65G20 PDFBibTeX XMLCite \textit{F. Bünger}, J. Comput. Appl. Math. 368, Article ID 112511, 20 p. (2020; Zbl 1429.65144) Full Text: DOI
Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T. Constructive error estimates for full discrete approximation of periodic solution for heat equation. (English) Zbl 1440.65141 J. Comput. Appl. Math. 368, Article ID 112510, 10 p. (2020). MSC: 65M60 65M15 65M22 35K55 35K05 65N30 PDFBibTeX XMLCite \textit{T. Kimura} et al., J. Comput. Appl. Math. 368, Article ID 112510, 10 p. (2020; Zbl 1440.65141) Full Text: DOI arXiv
Kepley, Shane; Mireles James, J. D. Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set. (English) Zbl 1451.70033 Celest. Mech. Dyn. Astron. 131, No. 3, Paper No. 13, 55 p. (2019). MSC: 70F15 70K44 34C45 PDFBibTeX XMLCite \textit{S. Kepley} and \textit{J. D. Mireles James}, Celest. Mech. Dyn. Astron. 131, No. 3, Paper No. 13, 55 p. (2019; Zbl 1451.70033) Full Text: DOI
van den Berg, Jan Bouwe; Williams, J. F. Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions. (English) Zbl 1409.35080 SIAM J. Math. Anal. 51, No. 1, 131-158 (2019). MSC: 35J60 35Q74 65N35 PDFBibTeX XMLCite \textit{J. B. van den Berg} and \textit{J. F. Williams}, SIAM J. Math. Anal. 51, No. 1, 131--158 (2019; Zbl 1409.35080) Full Text: DOI
Wanner, Thomas Computer-assisted bifurcation diagram validation and applications in materials science. (English) Zbl 1406.35040 van den Berg, Jan Bouwe (ed.) et al., Rigorous numerics in dynamics. AMS short course, Seattle, WA, USA, January 4–5, 2016. Lecture notes. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2814-3/hbk; 978-1-4704-4729-8/ebook). Proceedings of Symposia in Applied Mathematics 74, 123-174 (2018). MSC: 35B32 35B40 35B41 35K55 65G20 65G30 65P30 74N99 PDFBibTeX XMLCite \textit{T. Wanner}, Proc. Symp. Appl. Math. 74, 123--174 (2018; Zbl 1406.35040) Full Text: DOI
Lessard, Jean-Philippe Computing discrete convolutions with verified accuracy via Banach algebras and the FFT. (English) Zbl 1488.42047 Appl. Math., Praha 63, No. 3, 219-235 (2018). Reviewer: Manfred Tasche (Rostock) MSC: 42A85 42A05 65T50 65G40 46B45 46J15 42B05 35K35 PDFBibTeX XMLCite \textit{J.-P. Lessard}, Appl. Math., Praha 63, No. 3, 219--235 (2018; Zbl 1488.42047) Full Text: DOI
Breden, Maxime; Lessard, Jean-Philippe Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs. (English) Zbl 1398.65092 Discrete Contin. Dyn. Syst., Ser. B 23, No. 7, 2825-2858 (2018). MSC: 65G20 65P99 65D30 37M99 37C27 PDFBibTeX XMLCite \textit{M. Breden} and \textit{J.-P. Lessard}, Discrete Contin. Dyn. Syst., Ser. B 23, No. 7, 2825--2858 (2018; Zbl 1398.65092) Full Text: DOI arXiv
Castelli, Roberto; Garrione, Maurizio Some unexpected results on the Brillouin singular equation: fold bifurcation of periodic solutions. (English) Zbl 1415.34078 J. Differ. Equations 265, No. 6, 2502-2543 (2018). Reviewer: Alessandro Calamai (Ancona) MSC: 34C25 34B16 37M20 34C23 47N20 PDFBibTeX XMLCite \textit{R. Castelli} and \textit{M. Garrione}, J. Differ. Equations 265, No. 6, 2502--2543 (2018; Zbl 1415.34078) Full Text: DOI
Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation. (English) Zbl 1390.35262 Arch. Ration. Mech. Anal. 228, No. 1, 129-157 (2018). MSC: 35Q35 76B15 35R25 35B10 42A63 65M70 PDFBibTeX XMLCite \textit{R. Castelli} et al., Arch. Ration. Mech. Anal. 228, No. 1, 129--157 (2018; Zbl 1390.35262) Full Text: DOI arXiv
Lessard, Jean-Philippe; Sander, Evelyn; Wanner, Thomas Rigorous continuation of bifurcation points in the diblock copolymer equation. (English) Zbl 1404.35030 J. Comput. Dyn. 4, No. 1-2, 71-118 (2017). MSC: 35B32 35B40 65G20 65P30 35B41 35K55 65G30 65N35 74N99 58E09 35K35 PDFBibTeX XMLCite \textit{J.-P. Lessard} et al., J. Comput. Dyn. 4, No. 1--2, 71--118 (2017; Zbl 1404.35030) Full Text: DOI
Castelli, Roberto; Teismann, Holger Rigorous numerics for NLS: bound states, spectra, and controllability. (English) Zbl 1417.65193 Physica D 334, 158-173 (2016). MSC: 65N25 93B05 35Q55 93C20 65L15 PDFBibTeX XMLCite \textit{R. Castelli} and \textit{H. Teismann}, Physica D 334, 158--173 (2016; Zbl 1417.65193) Full Text: DOI arXiv Link
Watanabe, Yoshitaka; Nakao, Mitsuhiro T. A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. (English) Zbl 1410.65228 Appl. Math. Comput. 276, 239-251 (2016). MSC: 65J15 35B25 35J40 35J91 47F05 PDFBibTeX XMLCite \textit{Y. Watanabe} and \textit{M. T. Nakao}, Appl. Math. Comput. 276, 239--251 (2016; Zbl 1410.65228) Full Text: DOI
Correc, Anaïs; Lessard, Jean-Philippe Coexistence of nontrivial solutions of the one-dimensional Ginzburg-Landau equation: a computer-assisted proof. (English) Zbl 1384.34030 Eur. J. Appl. Math. 26, No. 1, 33-60 (2015). MSC: 34B15 65L10 82D55 PDFBibTeX XMLCite \textit{A. Correc} and \textit{J.-P. Lessard}, Eur. J. Appl. Math. 26, No. 1, 33--60 (2015; Zbl 1384.34030) Full Text: DOI
Birrell, Jeremiah A posteriori error bounds for two point boundary value problems: a Green’s function approach. (English) Zbl 1366.37050 J. Comput. Dyn. 2, No. 2, 143-164 (2015). MSC: 37C27 65G20 34B15 34B27 65L10 65L11 65L70 PDFBibTeX XMLCite \textit{J. Birrell}, J. Comput. Dyn. 2, No. 2, 143--164 (2015; Zbl 1366.37050) Full Text: DOI arXiv
Cai, Shuting; Watanabe, Yoshitaka A computer-assisted method for excluding eigenvalues of an elliptic operator linearized at a solution of a nonlinear problem. (English) Zbl 1333.35140 Japan J. Ind. Appl. Math. 32, No. 1, 263-294 (2015). MSC: 35P30 65N25 35J57 47A10 PDFBibTeX XMLCite \textit{S. Cai} and \textit{Y. Watanabe}, Japan J. Ind. Appl. Math. 32, No. 1, 263--294 (2015; Zbl 1333.35140) Full Text: DOI
van den Berg, J. B.; Groothedde, C. M.; Williams, J. F. Rigorous computation of a radially symmetric localized solution in a Ginzburg-Landau problem. (English) Zbl 1319.34048 SIAM J. Appl. Dyn. Syst. 14, No. 1, 423-447 (2015). MSC: 34B40 35Q56 34B16 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., SIAM J. Appl. Dyn. Syst. 14, No. 1, 423--447 (2015; Zbl 1319.34048) Full Text: DOI Link
Walter, Éric Numerical methods and optimization. A consumer guide. (English) Zbl 1328.65006 Cham: Springer (ISBN 978-3-319-07670-6/hbk; 978-3-319-07671-3/ebook). xv, 476 p. (2014). Reviewer: Octavian Pastravanu (Iaşi) MSC: 65-01 00A06 90-01 00A69 65Dxx 65Fxx 65Hxx 65Kxx 65Lxx 65Mxx 65Nxx PDFBibTeX XMLCite \textit{É. Walter}, Numerical methods and optimization. A consumer guide. Cham: Springer (2014; Zbl 1328.65006) Full Text: DOI
Lessard, Jean-Philippe; Reinhardt, Christian Rigorous numerics for nonlinear differential equations using Chebyshev series. (English) Zbl 1290.65060 SIAM J. Numer. Anal. 52, No. 1, 1-22 (2014). MSC: 65L05 34A34 65L10 34B15 PDFBibTeX XMLCite \textit{J.-P. Lessard} and \textit{C. Reinhardt}, SIAM J. Numer. Anal. 52, No. 1, 1--22 (2014; Zbl 1290.65060) Full Text: DOI
Antal, Elvira; Csendes, Tibor; Virágh, János Nonlinear transformations for the simplification of unconstrained nonlinear optimization problems. (English) Zbl 1339.90010 CEJOR, Cent. Eur. J. Oper. Res. 21, No. 4, 665-684 (2013). MSC: 90-04 90C26 68W30 13P25 PDFBibTeX XMLCite \textit{E. Antal} et al., CEJOR, Cent. Eur. J. Oper. Res. 21, No. 4, 665--684 (2013; Zbl 1339.90010) Full Text: DOI
Li, Qingdu; Tang, Song; Yang, Xiao-Song New bifurcations in the simplest passive walking model. (English) Zbl 1331.70021 Chaos 23, No. 4, 043110, 14 p. (2013). MSC: 70E60 70K50 70K55 37N20 92C10 PDFBibTeX XMLCite \textit{Q. Li} et al., Chaos 23, No. 4, 043110, 14 p. (2013; Zbl 1331.70021) Full Text: DOI
Fazal, Qaisra; Neumaier, Arnold Error bounds for initial value problems by optimization. (English) Zbl 1327.65148 Soft Comput. 17, No. 8, 1345-1356 (2013). MSC: 65L70 65L05 34A34 65K05 90C26 65F08 PDFBibTeX XMLCite \textit{Q. Fazal} and \textit{A. Neumaier}, Soft Comput. 17, No. 8, 1345--1356 (2013; Zbl 1327.65148) Full Text: DOI
Dohnal, Tomáš; Nagatou, Kaori; Plum, Michael; Reichel, Wolfgang Interfaces supporting surface gap soliton ground states in the 1D nonlinear Schrödinger equation. (English) Zbl 1315.34097 J. Math. Anal. Appl. 407, No. 2, 425-435 (2013). MSC: 34L40 78A40 58E50 34B10 81Q05 PDFBibTeX XMLCite \textit{T. Dohnal} et al., J. Math. Anal. Appl. 407, No. 2, 425--435 (2013; Zbl 1315.34097) Full Text: DOI arXiv
Pál, László; Csendes, Tibor An intlab based global optimization method and its application to a sensor network localization problem. (Hungarian. English summary) Zbl 1289.90201 Alkalmazott Mat. Lapok 28, 17-40 (2011). MSC: 90C30 90-08 PDFBibTeX XMLCite \textit{L. Pál} and \textit{T. Csendes}, Alkalmazott Mat. Lapok 28, 17--40 (2011; Zbl 1289.90201)
van den Berg, Jan Bouwe; Mireles-James, Jason D.; Lessard, Jean-Philippe; Mischaikow, Konstantin Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation. (English) Zbl 1231.34081 SIAM J. Math. Anal. 43, No. 4, 1557-1594 (2011). MSC: 34C37 34A45 34B15 47N20 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., SIAM J. Math. Anal. 43, No. 4, 1557--1594 (2011; Zbl 1231.34081) Full Text: DOI
Chen, Xiaojun; Frommer, Andreas; Lang, Bruno Computational existence proofs for spherical \(t\)-designs. (English) Zbl 1208.65032 Numer. Math. 117, No. 2, 289-305 (2011). MSC: 65D32 41A55 41A63 65H10 65G30 65G20 PDFBibTeX XMLCite \textit{X. Chen} et al., Numer. Math. 117, No. 2, 289--305 (2011; Zbl 1208.65032) Full Text: DOI
Rump, Siegfried M.; Graillat, Stef Verified error bounds for multiple roots of systems of nonlinear equations. (English) Zbl 1201.65081 Numer. Algorithms 54, No. 3, 359-377 (2010). Reviewer: Svetoslav Markov (Sofia) MSC: 65H10 65G20 65H04 65F15 PDFBibTeX XMLCite \textit{S. M. Rump} and \textit{S. Graillat}, Numer. Algorithms 54, No. 3, 359--377 (2010; Zbl 1201.65081) Full Text: DOI
Shibayama, Mitsuru; Yagasaki, Kazuyuki Heteroclinic connections between triple collisions and relative periodic orbits in the isosceles three-body problem. (English) Zbl 1173.70006 Nonlinearity 22, No. 10, 2377-2403 (2009). MSC: 70F07 70K44 70K42 70F16 PDFBibTeX XMLCite \textit{M. Shibayama} and \textit{K. Yagasaki}, Nonlinearity 22, No. 10, 2377--2403 (2009; Zbl 1173.70006) Full Text: DOI Link
Moore, Ramon E.; Kearfott, R. Baker; Cloud, Michael J. Introduction to interval analysis. (English) Zbl 1168.65002 Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-69-6/pbk; 978-0-89871-771-6/ebook). xi, 223 p. (2009). Reviewer: Günter Mayer (Rostock) MSC: 65-01 65G30 65G50 65Fxx 65Hxx 65R20 65Lxx 65G20 68W30 PDFBibTeX XMLCite \textit{R. E. Moore} et al., Introduction to interval analysis. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2009; Zbl 1168.65002) Full Text: DOI Link
Maier-Paape, Stanislaus; Miller, Ulrich; Mischaikow, Konstantin; Wanner, Thomas Rigorous numerics for the Cahn-Hilliard equation on the unit square. (English) Zbl 1160.37418 Rev. Mat. Complut. 21, No. 2, 351-426 (2008). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37L10 35K35 35B05 35K55 PDFBibTeX XMLCite \textit{S. Maier-Paape} et al., Rev. Mat. Complut. 21, No. 2, 351--426 (2008; Zbl 1160.37418) Full Text: DOI EuDML
Nakao, Mitsuhiro T.; Hashimoto, Kouji Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications. (English) Zbl 1154.65081 J. Comput. Appl. Math. 218, No. 1, 106-115 (2008). Reviewer: Fumio Kikuchi (Tokyo) MSC: 65N15 65N30 35J25 35J65 35R05 PDFBibTeX XMLCite \textit{M. T. Nakao} and \textit{K. Hashimoto}, J. Comput. Appl. Math. 218, No. 1, 106--115 (2008; Zbl 1154.65081) Full Text: DOI
Alefeld, Götz; Wang, Zhengyu Error estimation for nonlinear complementarity problems via linear systems with interval data. (English) Zbl 1154.90016 Numer. Funct. Anal. Optim. 29, No. 3-4, 243-267 (2008). Reviewer: Igor V. Konnov (Kazan) MSC: 90C33 65G30 65K10 PDFBibTeX XMLCite \textit{G. Alefeld} and \textit{Z. Wang}, Numer. Funct. Anal. Optim. 29, No. 3--4, 243--267 (2008; Zbl 1154.90016) Full Text: DOI Link
Wang, Zhengyu Extensions of Kantorovich theorem to complementarity problem. (English) Zbl 1225.90139 ZAMM, Z. Angew. Math. Mech. 88, No. 3, 179-190 (2008). Reviewer: Igor V. Konnov (Kazan) MSC: 90C33 65K15 PDFBibTeX XMLCite \textit{Z. Wang}, ZAMM, Z. Angew. Math. Mech. 88, No. 3, 179--190 (2008; Zbl 1225.90139) Full Text: DOI
Ryoo, Cheon Seoung An approach to the numerical verification of solutions for obstacle problems. (English) Zbl 1133.49013 Comput. Math. Appl. 53, No. 5, 842-850 (2007). MSC: 49J40 90C33 47H10 47J20 PDFBibTeX XMLCite \textit{C. S. Ryoo}, Comput. Math. Appl. 53, No. 5, 842--850 (2007; Zbl 1133.49013) Full Text: DOI
Yamamoto, Nobito; Genma, Kenta On error estimation of finite element approximations to the elliptic equations in nonconvex polygonal domains. (English) Zbl 1108.65109 J. Comput. Appl. Math. 199, No. 2, 286-296 (2007). MSC: 65N15 65N30 35J65 PDFBibTeX XMLCite \textit{N. Yamamoto} and \textit{K. Genma}, J. Comput. Appl. Math. 199, No. 2, 286--296 (2007; Zbl 1108.65109) Full Text: DOI
Hashimoto, Kouji; Kobayashi, Kenta; Nakao, Mitsuhiro T. Numerical verification methods for solutions of the free boundary problem. (English) Zbl 1081.65081 Numer. Funct. Anal. Optimization 26, No. 4-5, 523-542 (2005). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65L60 65L10 34B15 65G20 PDFBibTeX XMLCite \textit{K. Hashimoto} et al., Numer. Funct. Anal. Optim. 26, No. 4--5, 523--542 (2005; Zbl 1081.65081) Full Text: DOI Link
Nakao, M. T.; Hashimoto, K.; Watanabe, Y. A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. (English) Zbl 1151.35337 Computing 75, No. 1, 1-14 (2005). MSC: 35J25 35J60 65N25 PDFBibTeX XMLCite \textit{M. T. Nakao} et al., Computing 75, No. 1, 1--14 (2005; Zbl 1151.35337) Full Text: DOI Link
Hashimoto, Kouji; Abe, Ryohei; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka A numerical verification method for solutions of singularly perturbed problems with nonlinearity. (English) Zbl 1071.65110 Japan J. Ind. Appl. Math. 22, No. 1, 111-131 (2005). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L10 65L60 34B15 34E15 65G20 68T15 PDFBibTeX XMLCite \textit{K. Hashimoto} et al., Japan J. Ind. Appl. Math. 22, No. 1, 111--131 (2005; Zbl 1071.65110) Full Text: DOI
Jaulin, Luc; Kieffer, Michel; Didrit, Olivier; Walter, Éric Applied interval analysis. With examples in parameter and state estimation, robust control and robotics. Incl. 1 CD-ROM. (English) Zbl 1023.65037 London: Springer. xvi, 379 p. (2001). Reviewer: Vladik Ya.Kreinovich (El Paso) MSC: 65G40 65-02 65G20 65G30 70E60 65K05 90C30 62F10 65C60 93B30 93D09 PDFBibTeX XMLCite \textit{L. Jaulin} et al., Applied interval analysis. With examples in parameter and state estimation, robust control and robotics. Incl. 1 CD-ROM. London: Springer (2001; Zbl 1023.65037)