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Volume 2, Issue 1
Correction Procedure for Solving Partial Differential Equations

Qun Lin & Lü Tao

J. Comp. Math., 2 (1984), pp. 56-69.

Published online: 1984-02

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  • Abstract

The correction procedure has been discussed by L. Fox and V. Pereyra for accelerating the convergence of a certain approximate solution. Its theoretical basis is the existence of an asymptotic expansion for the error of discretization proved by Filippov and Rybinskii and Stetter: $u-u_h=h^2 v+O(h^4)$, where $u$ is the solution of the original differential equation, $u_h$ the solution of the approximate finite difference equation with parameter $h$ and $v$ the solution of a correction differential equation independent of $h$. Stetter et al. used the extrapolation procedure to eliminate the auxiliary function $v$ while Pereyra et al. used some special procedure to solve v approximately.  
In the present paper we will present a difference procedure for solving $v$ easily.  

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@Article{JCM-2-56, author = {Lin , Qun and Tao , Lü}, title = {Correction Procedure for Solving Partial Differential Equations}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {1}, pages = {56--69}, abstract = {

The correction procedure has been discussed by L. Fox and V. Pereyra for accelerating the convergence of a certain approximate solution. Its theoretical basis is the existence of an asymptotic expansion for the error of discretization proved by Filippov and Rybinskii and Stetter: $u-u_h=h^2 v+O(h^4)$, where $u$ is the solution of the original differential equation, $u_h$ the solution of the approximate finite difference equation with parameter $h$ and $v$ the solution of a correction differential equation independent of $h$. Stetter et al. used the extrapolation procedure to eliminate the auxiliary function $v$ while Pereyra et al. used some special procedure to solve v approximately.  
In the present paper we will present a difference procedure for solving $v$ easily.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9640.html} }
TY - JOUR T1 - Correction Procedure for Solving Partial Differential Equations AU - Lin , Qun AU - Tao , Lü JO - Journal of Computational Mathematics VL - 1 SP - 56 EP - 69 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9640.html KW - AB -

The correction procedure has been discussed by L. Fox and V. Pereyra for accelerating the convergence of a certain approximate solution. Its theoretical basis is the existence of an asymptotic expansion for the error of discretization proved by Filippov and Rybinskii and Stetter: $u-u_h=h^2 v+O(h^4)$, where $u$ is the solution of the original differential equation, $u_h$ the solution of the approximate finite difference equation with parameter $h$ and $v$ the solution of a correction differential equation independent of $h$. Stetter et al. used the extrapolation procedure to eliminate the auxiliary function $v$ while Pereyra et al. used some special procedure to solve v approximately.  
In the present paper we will present a difference procedure for solving $v$ easily.  

Lin , Qun and Tao , Lü. (1984). Correction Procedure for Solving Partial Differential Equations. Journal of Computational Mathematics. 2 (1). 56-69. doi:
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