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

Abstract EN

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.