文章基本信息

标题：Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values
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作者：Liyun Su ; Tianshun Yan ; Yanyong Zhao 等
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2012
卷号：2012
DOI：10.1155/2012/201678
出版社：Hindawi Publishing Corporation
摘要：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.