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- Title
Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values.
- Authors
Liyun Su; Tianshun Yan; Yanyong Zhao; Fenglan Li
- Abstract
Local polynomial regressionLPR is applied to solve the partial differential equationsPDEs. 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.
- Subjects
POLYNOMIALS; REGRESSION analysis; EIGENFUNCTION expansions; BOUNDARY value problems; EIGENFUNCTIONS
- Publication
Discrete Dynamics in Nature & Society, 2012, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2012/201678