A defect correction method for functional equations

1976 ◽  
pp. 16-29 ◽  
Author(s):  
K. Böhmer
Keyword(s):  
Functional Equations ◽  
Correction Method ◽  
Defect Correction

THE PARAMETER-ROBUST NUMERICAL METHOD BASED ON DEFECT-CORRECTION TECHNIQUE FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH LAYER BEHAVIOR

2010 ◽  
Vol 07 (04) ◽  
pp. 573-594 ◽  
Author(s):  
JUGAL MOHAPATRA ◽  
SRINIVASAN NATESAN
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Perturbation Parameter ◽  
Correction Method ◽  
Singularly Perturbed ◽  
Defect Correction ◽  
Central Difference ◽  
Correction Technique ◽  
Delay Differential

In this article, we consider a defect-correction method based on finite difference scheme for solving a singularly perturbed delay differential equation. We solve the equation using upwind finite difference scheme on piecewise-uniform Shishkin mesh, then apply the defect-correction technique that combines the stability of the upwind scheme and the higher-order central difference scheme. The method is shown to be convergent uniformly in the perturbation parameter and almost second-order convergence measured in the discrete maximum norm is obtained. Numerical results are presented, which are in agreement with the theoretical findings.

Further analysis of the local defect correction method

Computing ◽  
1996 ◽  
Vol 56 (2) ◽  
pp. 117-139 ◽  
Author(s):  
P. J. J. Ferket ◽  
A. A. Reusken
Keyword(s):  
Correction Method ◽  
Local Defect ◽  
Defect Correction

A Defect Correction Method for Multi-Scale Problems in Computational Aeroacoustics

2002 ◽  
pp. 147-156
Author(s):  
Georgi S. Djambazov ◽  
Choi-Hong Lai ◽  
Koulis A. Pericleous ◽  
Zong-Kang Wang
Keyword(s):  
Correction Method ◽  
Computational Aeroacoustics ◽  
Defect Correction ◽  
Multi Scale

Convergence analysis of the local defect correction method for diffusion equations

2003 ◽  
Vol 95 (3) ◽  
pp. 401-425 ◽  
Author(s):  
M.J.H. Anthonissen ◽  
R.M.M. Mattheij ◽  
J.H.M. ten Thije Boonkkamp
Keyword(s):  
Convergence Analysis ◽  
Correction Method ◽  
Diffusion Equations ◽  
Local Defect ◽  
Defect Correction

A Multigrid Solver based on Distributive Smoother and Residual Overweighting for Oseen Problems

2015 ◽  
Vol 8 (2) ◽  
pp. 237-252 ◽  
Author(s):  
Long Chen ◽  
Xiaozhe Hu ◽  
Ming Wang ◽  
Jinchao Xu
Keyword(s):  
Least Squares ◽  
Correction Method ◽  
Numerical Results ◽  
Staggered Grid ◽  
Defect Correction ◽  
Multigrid Solver ◽  
Mac Scheme

AbstractAn efficient multigrid solver for the Oseen problems discretized by Marker and Cell (MAC) scheme on staggered grid is developed in this paper. Least squares commutator distributive Gauss-Seidel (LSC-DGS) relaxation is generalized and developed for Oseen problems. Residual overweighting technique is applied to further improve the performance of the solver and a defect correction method is suggested to improve the accuracy of the discretization. Some numerical results are presented to demonstrate the efficiency and robustness of the proposed solver.

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