@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 = {<p style="text-align: justify;">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. &nbsp;<br/>In the present paper we will present a difference procedure for solving $v$ easily. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9640.html}
}