Gaussian collocation via defect correction

DOI10.1007/BF01385631zbMath0722.65043MaRDI QIDQ756383

Karl-Heinz Schild

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133507

zbMATH Keywords

superconvergencedefect correction methodorder of accuracyfirst order systemsGaussian collocation

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (5)

Local error estimates for moderately smooth problems. I: ODEs and DAEs ⋮ Deferred correction methods for ordinary differential equations ⋮ Faster SDC convergence on non-equidistant grids by DIRK sweeps ⋮ Analysis of a defect correction method for geometric integrators ⋮ Arbitrary high order A-stable and B-convergent numerical methods for ODEs via deferred correction

Cites Work

• Unnamed Item
• IDeC-convergence independent of error asymptotics
• Deferred corrections using uncentered end formulas
• Discrete Newton methods and iterated defect corrections
• Perturbed collocation and Runge-Kutta methods
• The defect correction principle and discretization methods
• The Stability of One-Step Schemes for First-Order Two-Pointv Boundary Value Problems
• The Order of Accuracy for Deferred Corrections Using Uncentered End Formulas
• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• A Collocation Solver for Mixed Order Systems of Boundary Value Problems
• The Application of Implicit Runge-Kutta and Collocation Methods to Boundary-Value Problems
• Collocation at Gaussian Points

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