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 - <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>