ANALYSIS OF A FOURTH ORDER SCHEME AND APPLICATION OF LOCAL DEFECT CORRECTION METHOD

2014 ◽  
Vol 32 (3_4) ◽  
pp. 511-527
Author(s):  
Ali Abbas
Keyword(s):  
Fourth Order ◽  
Correction Method ◽  
Local Defect ◽  
Defect Correction ◽  
Order Scheme

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

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 finite volume local defect correction method for solving the transport equation

2009 ◽  
Vol 38 (3) ◽  
pp. 533-543 ◽  
Author(s):  
W. Kramer ◽  
R. Minero ◽  
H.J.H. Clercx ◽  
R.M.M. Mattheij
Keyword(s):  
Transport Equation ◽  
Finite Volume ◽  
Correction Method ◽  
Local Defect ◽  
Defect Correction

scholarly journals Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem

2021 ◽  
Author(s):  
Fei Xu ◽  
Liu Chen ◽  
Qiumei Huang
Keyword(s):  
Eigenvalue Problem ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Correction Method ◽  
Small Scale ◽  
Local Defect ◽  
Defect Correction ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Steklov Eigenvalue Problems

In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on the multilevel discretization. The objective is to avoid solving large-scale equations especially the large-scale Steklov eigenvalue problem whose computational cost increases exponentially. The proposed algorithm transforms the Steklov eigenvalue problem into a series of linear boundary value problems, which are defined in a multigrid space sequence, and a series of small-scale Steklov eigenvalue problems in a coarse correction space. Furthermore, we use the local defect-correction technique to divide the large-scale boundary value problems into small-scale subproblems. Through our proposed algorithm, we avoid solving large-scale Steklov eigenvalue problems. As a result, our proposed algorithm demonstrates significantly improved the solving efficiency. Additionally, we conduct numerical experiments and a rigorous theoretical analysis to verify the effectiveness of our proposed approach.

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.

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