Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations

DOI10.1016/S0377-0427(00)00563-XzbMath0998.65099MaRDI QIDQ5949506

Teruya Minamoto

Publication date: 21 November 2001

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

zbMATH Keywords

numerical examplesfinite elementinitial-boundary value problemscomputer-assisted methodguaranteed error boundsnonlinear wave equations

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Algorithms with automatic result verification (65G20)

Related Items (2)

Rigorous numerical computations for 1D advection equations with variable coefficients ⋮ Numerical existence and uniqueness proof for solutions of semilinear parabolic equations

Cites Work

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• On computational proofs of the existence of solutions to nonlinear parabolic problems
• Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case
• Numerical verification of solutions for nonlinear hyperbolic equations
• Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods
• Real Interpolation of Sobolev Spaces on Subdomains of Rn
• A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
• An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness

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