Cosine methods for a class of semilinear second-order wave equations

DOI10.1016/0898-1221(90)90355-NzbMath0704.65068OpenAlexW2066750036MaRDI QIDQ917239

Charalambos G. Makridakis

Publication date: 1990

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(90)90355-n

zbMATH Keywords

convergenceoptimal error estimatesGalerkin methodssecond-order wave equationscosine methodsemilinear hyperbolic wave equations

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Second-order nonlinear hyperbolic equations (35L70) 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)

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Cites Work

• Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics
• Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations
• An approximation theorem for second-order evolution equations
• Cosine Methods for Second-Order Hyperbolic Equations With Time-Dependent Coefficients
• Cosine Methods for Nonlinear Second-Order Hyperbolic Equations
• Efficient Higher Order Single Step Methods for Parabolic Problems: Part I
• Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations