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

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