Order reduction and how to avoid it when explicit Runge-Kutta-Nyström methods are used to solve linear partial differential equations

DOI10.1016/j.cam.2004.07.021zbMath1069.65101OpenAlexW1999382259MaRDI QIDQ1763654

M. J. Moreta, Begoña Cano, Isaías Alonso-Mallo

Publication date: 22 February 2005

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.2004.07.021

zbMATH Keywords

numerical experimentsRunge-Kutta-Nyström methodsmethod of linesinitial-boundary value problemsorder reductionlinear second order hyperbolic equations

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for second-order hyperbolic equations (35L15)

Related Items

Stability of Runge-Kutta-Nyström methods, Analysis of order reduction when integrating linear initial boundary value problems with Lawson methods, Boundary treatment of implicit-explicit Runge-Kutta method for hyperbolic systems with source terms, A spectral deferred correction method for incompressible flow with variable viscosity, Numerical methods for nonlinear second-order hyperbolic partial differential equations. II: Rothe's techniques for 1-D problems, Stable Runge-Kutta-Nyström methods for dissipative stiff problems, Optimal time order when implicit Runge-Kutta-Nyström methods solve linear partial differential equations, Avoiding the order reduction when solving second-order in time PDEs with fractional step Runge-Kutta-Nyström methods, Projected explicit lawson methods for the integration of Schrödinger equation, Stability and convergence of staggered Runge-Kutta schemes for semilinear wave equations, A modified Gautschi's method without order reduction when integrating boundary value nonlinear wave problems

Uses Software

• RODAS

Cites Work

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