Modified Adomian Decomposition Method for Van der Pol equations

Highlights

• Using MADM, we solved non-linear problems for VDP non-linear equations.

• MADM results agree with the numerical solutions.

• We solved different types of problems to confirm the robustness of the present method.

• A number of non-linear problems in VDP equations are encountered in engineering applications which are solved effectively.

Abstract

In the paper, the well known Adomian Decomposition Method (ADM) is modified to solve the parabolic equations. The present method is quite different than the numerical method. The results are compared with the existing exact or analytical method. The already known existing Adomian Decomposition Method is modified to improve the accuracy and convergence. Thus, the modified method is named as Modified Adomian Decomposition Method (MADM). The Modified Adomian Decomposition Method results are found to converge very quickly and are more accurate compared to ADM and numerical methods. MADM is quite efficient and is practically well suited for use in these problems. Several examples are given to check the reliability of the present method. Modified Adomian Decomposition Method is a non-numerical method which can be adapted for solving parabolic equations. In the current paper, the principle of the decomposition method is described, and its advantages are shown in the form of parabolic equations.