Iterated Defect Correction for the Solution of Singular Initial Value Problems

DOI10.1137/S0036142900368095zbMath0989.65068OpenAlexW2027382177MaRDI QIDQ2706389

Othmar Koch, Ewa B. Weinmüller

Publication date: 19 March 2001

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142900368095

zbMATH Keywords

convergenceconvergence accelerationinitial value problemsiterated defect correctionsingularity of the first kindimplicit Euler rule

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (23)

The convergence of shooting methods for singular boundary value problems ⋮ A semi‐discrete defect correction finite element method for unsteady incompressible magnetohydrodynamics equations ⋮ On numerical methods to second-order singular initial value problems with additive white noise ⋮ Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods ⋮ On a singular boundary value problem arising in the theory of shallow membrane caps ⋮ Optimal solution of a class of non-autonomous initial-value problems with unknown singularities ⋮ A defect-correction mixed finite element method for stationary conduction-convection problems ⋮ Implicit methods for numerical solution of singular initial value problems ⋮ Analytical and numerical treatment of a singular initial value problem in avalanche modeling. ⋮ Complexity of the derivative-free solution of systems of IVPs with unknown singularity hypersurface ⋮ Second order modified method of characteristics mixed defect-correction finite element method for time dependent Navier-Stokes problems ⋮ Defect correction finite element method for the stationary incompressible magnetohydrodynamics equation ⋮ Optimal adaptive solution of initial-value problems with unknown singularities ⋮ Optimal adaptive solution of piecewise regular systems of IVPs with unknown switching hypersurface ⋮ Linearization techniques for singular initial-value problems of ordinary differential equations ⋮ Asymptotically correct error estimation for collocation methods applied to singular boundary value problems ⋮ A defect-correction method for unsteady conduction-convection problems. I: Spatial discretization ⋮ A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations ⋮ Piecewise quasilinearization techniques for singular boundary-value problems ⋮ Error estimate of a fully discrete defect correction finite element method for unsteady incompressible Magnetohydrodynamics equations ⋮ The adapted block boundary value methods for singular initial value problems ⋮ Modified characteristics mixed defect-correction finite element method for the time-dependent Navier–Stokes problems ⋮ A defect-correction method for unsteady conduction-convection problems. II: Time discretization

Uses Software

• avalanche.f

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