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.
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.