Convergence analysis of one-step schemes in the method of lines

DOI10.1016/0096-3003(89)90118-5zbMath0671.65077OpenAlexW2580626451MaRDI QIDQ1119363

Jan G. Verwer, Jesús María Sanz-Serna

Publication date: 1989

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

Full work available at URL: https://ir.cwi.nl/pub/1698

zbMATH Keywords

convergencenumerical exampleconsistencymethod of linesevolution equationsnumerical stabilityorder reductioncontractivity

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (10)

Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups ⋮ Stability and convergence at the PDE/stiff ODE interface ⋮ Strong stability preserving general linear methods ⋮ Construction of higher order symplectic schemes by composition ⋮ Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods ⋮ An easily implementable fourth-order method for the time integration of wave problems ⋮ Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods ⋮ Infinite Systems of Quasilinear Differential Difference Inequalities and Applications ⋮ STRONG STABILITY PRESERVING MULTISTAGE INTEGRATION METHODS ⋮ Consistency and stability for some nonnegativity-conserving methods

Cites Work

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• Über Die Stabilitätsdefinition Für Differenzengleichungen Die Partielle Differentialgleichungen Approximieren
• Single step methods for inhomogeneous linear differential equations in Banach space
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• Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet

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