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Volume 11, Issue 4
Spline Finite Difference Methods and Their Extrapolation for Singular Two-Point Boundary Value Problems

Guo-Qiang Han

J. Comp. Math., 11 (1993), pp. 289-296.

Published online: 1993-11

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  • Abstract

In this paper we consider a class of singular two-point boundary value problem: $(x^αu')'=f(x,u),u(0)=A,u(1)=B,0＜α＜1$. The asymptotic expression of the spline finite difference solution for the problem is obtained. By using the asymptotic expression, Richardson's extrapolation can be done and the accuracy of numerical solution can be improved. Some numerical examples are given in illustration of this theory.  

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@Article{JCM-11-289, author = {Han , Guo-Qiang}, title = {Spline Finite Difference Methods and Their Extrapolation for Singular Two-Point Boundary Value Problems}, journal = {Journal of Computational Mathematics}, year = {1993}, volume = {11}, number = {4}, pages = {289--296}, abstract = {

In this paper we consider a class of singular two-point boundary value problem: $(x^αu')'=f(x,u),u(0)=A,u(1)=B,0＜α＜1$. The asymptotic expression of the spline finite difference solution for the problem is obtained. By using the asymptotic expression, Richardson's extrapolation can be done and the accuracy of numerical solution can be improved. Some numerical examples are given in illustration of this theory.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9327.html} }
TY - JOUR T1 - Spline Finite Difference Methods and Their Extrapolation for Singular Two-Point Boundary Value Problems AU - Han , Guo-Qiang JO - Journal of Computational Mathematics VL - 4 SP - 289 EP - 296 PY - 1993 DA - 1993/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9327.html KW - AB -

In this paper we consider a class of singular two-point boundary value problem: $(x^αu')'=f(x,u),u(0)=A,u(1)=B,0＜α＜1$. The asymptotic expression of the spline finite difference solution for the problem is obtained. By using the asymptotic expression, Richardson's extrapolation can be done and the accuracy of numerical solution can be improved. Some numerical examples are given in illustration of this theory.  

Han , Guo-Qiang. (1993). Spline Finite Difference Methods and Their Extrapolation for Singular Two-Point Boundary Value Problems. Journal of Computational Mathematics. 11 (4). 289-296. doi:
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