Finding the approximate analytical solutions of 2n (nϵR) order differential equation with boundary value problem using various techniques

Abstract

This paper judges against the errors estimated by approximate analytical solutions obtained using homotopy perturbation method (HPM), and modified power series method. HPM is a combination of traditional perturbation method and the homotopy method. A numerical example has been considered to demonstrate the effectiveness, exactness and implementation of the method and the results of errors are compared. To attain sufficiently exact results with HPM, it is generally required to calculate at least two statements of the S -terms. However, it was exposed in the numerical examples that highly accurate results were obtained by calculating only one S-term of the series, revealing the effectiveness of the HPM solution. It is concluded that HPM is a powerful tool for solving high-order boundary value problem as it shows less error than MPSAM.