Improved convergence theorems of Newton's method designed for the numerical verification for solutions of differential equations

DOI10.1016/J.CAM.2005.08.035zbMath1112.65101OpenAlexW2118289812MaRDI QIDQ861902

Tadashi Kawanago

Publication date: 2 February 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.035

zbMATH Keywords

finite element methodcomputational efficiencynonlinear elliptic equationsnumerical verification

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Algorithms with automatic result verification (65G20)

Related Items (2)

Error analysis of Galerkin's method for semilinear equations ⋮ Codimension-\(m\) bifurcation theorems applicable to the numerical verification methods

Cites Work

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• Numerical verifications of solutions for nonlinear elliptic equations
• A symmetry-breaking bifurcation theorem and some related theorems applicable to maps having unbounded derivatives
• Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration
• An efficient approach to the numerical verification for solutions of elliptic differential equations
• A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems

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