In this article, a new homotopy technique is presented for the mathematical analysis of finding the solution of partial differential equation and we compare the decision of using NHPM with those using HPM to view the efficacy and advantageousness of the new capability. The purpose of this study is to show that constructing the proper homotopy in a correct way determines the solution with less computational work than using the existing approach while supplying quantitatively reliable results. To illustrate the capability and reliability of the method examples are provided. Comparison of the results of applying NHPM with those of applying HPM reveal the effectiveness and convenience of the new technique.