Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations

DOI10.1007/s00211-016-0810-5zbMath1359.65171OpenAlexW2186381545MaRDI QIDQ512166

Marlis Hochbruck, Tomislav Pažur

Publication date: 24 February 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-016-0810-5

zbMATH Keywords

convergencewave equationerror analysisimplicit Euler methodMaxwell equationabstract, quasilinear hyperbolic evolution equations

Mathematics Subject Classification ID

Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solutions to equations with nonlinear operators (65J15) Abstract hyperbolic equations (35L90) Numerical solutions to abstract evolution equations (65J08) Maxwell equations (35Q61)

Related Items (9)

Evolution equations governed by quasilinear operators satisfying Carathéodory’s conditions ⋮ On a splitting method for the Zakharov system ⋮ Trigonometric integrators for quasilinear wave equations ⋮ Exponential Integrators for Quasilinear Wave-Type Equations ⋮ Error analysis of implicit Runge-Kutta methods for quasilinear hyperbolic evolution equations ⋮ One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations ⋮ Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations ⋮ Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type ⋮ Global error bounds of one-stage extended RKN integrators for semilinear wave equations

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