Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 201678, 11 pages
http://dx.doi.org/10.1155/2012/201678
Research Article

Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values

Liyun Su,1 Tianshun Yan,1 Yanyong Zhao,1 and Fenglan Li2

1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
2Institute of Library, Chongqing University of Technology, Chongqing 400054, China

Received 15 April 2012; Accepted 29 July 2012

Academic Editor: Leonid Shaikhet

Copyright © 2012 Liyun Su et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Local polynomial regression (LPR) is applied to solve the partial differential equations (PDEs). Usually, the solutions of the problems are separation of variables and eigenfunction expansion methods, so we are rarely able to find analytical solutions. Consequently, we must try to find numerical solutions. In this paper, two test problems are considered for the numerical illustration of the method. Comparisons are made between the exact solutions and the results of the LPR. The results of applying this theory to the PDEs reveal that LPR method possesses very high accuracy, adaptability, and efficiency; more importantly, numerical illustrations indicate that the new method is much more efficient than B-splines and AGE methods derived for the same purpose.