Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems

DOI10.1090/S0025-5718-01-01362-XzbMath1005.65100OpenAlexW2019971825MaRDI QIDQ3147174

M. P. Calvo, César Palencia

Publication date: 18 September 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01362-x

zbMATH Keywords

numerical exampleBanach spaceRunge-Kutta methodorder reductionabstract initial boundary value problems

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solutions to equations with linear operators (65J10) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Linear differential equations in abstract spaces (34G10)

Related Items (21)

Analytical and numerical treatment of electro-thermo-mechanical coupling ⋮ Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions ⋮ Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions ⋮ Arbitrary order Krylov deferred correction methods for differential algebraic equations ⋮ Avoiding order reduction when integrating nonlinear Schrödinger equation with Strang method ⋮ Comparison of efficiency among different techniques to avoid order reduction with Strang splitting ⋮ Design of DIRK schemes with high weak stage order ⋮ Algebraic Structure of the Weak Stage Order Conditions for Runge–Kutta Methods ⋮ On time staggering for wave equations ⋮ On the Gauss Runge-Kutta and Method of Lines Transpose for Initial-Boundary Value Parabolic PDEs ⋮ Higher-order temporal integration for the incompressible Navier-Stokes equations in bounded domains ⋮ Avoiding the order reduction when solving second-order in time PDEs with fractional step Runge-Kutta-Nyström methods ⋮ Pseudospectral solution of linear evolution equations of second order in space and time on unstructured quadrilateral subdomain topologies ⋮ Accelerating the convergence of spectral deferred correction methods ⋮ Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations ⋮ Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems ⋮ Convolution quadrature time discretization of fractional diffusion-wave equations ⋮ High Order Implicit-explicit General Linear Methods with Optimized Stability Regions ⋮ Semi-implicit Krylov deferred correction methods for differential algebraic equations ⋮ Optimal orders of convergence for Runge-Kutta methods and linear, initial boundary value problems ⋮ Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems

Uses Software

• RODAS

Cites Work

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