Error estimates for deferred correction methods in time

DOI10.1016/j.apnum.2006.04.002zbMath1115.65098OpenAlexW2089956933MaRDI QIDQ870308

Wendy Kress

Publication date: 12 March 2007

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.04.002

zbMATH Keywords

stabilityerror estimatesboundary conditionsnumerical experimentsinitial boundary value problemsbackward differentiation formulaedeferred correctionimplicit midpoint rulehigh order time discretization

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (10)

A gradually implicit method with deferred correction and adaptive relaxation factors for simulation to nonlinear heat transfer ⋮ A fast and stable algorithm for linear parabolic partial differential equations ⋮ Boosting the accuracy of finite difference schemes via optimal time step selection and non-iterative defect correction ⋮ Grid adaptation and non-iterative defect correction for improved accuracy of numerical solutions of PDEs ⋮ An enhanced parareal algorithm based on the deferred correction methods for a stiff system ⋮ A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems ⋮ Numerical solution of multidimensional hyperbolic PDEs using defect correction on adaptive grids ⋮ High‐order TVB discretizations in time using Richardson's extrapolation ⋮ On the efficiency of spectral deferred correction methods for time-dependent partial differential equations ⋮ Variable-step deferred correction methods based on backward differentiation formulae for ordinary differential equations

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