Variational Iteration Homotopy Perturbation Method for the Solution of Seventh Order Boundary Value Problems

TL;DR

This paper introduces the Variational Iteration Homotopy Perturbation Method (VIHPM) for efficiently solving seventh order boundary value problems, demonstrated through numerical examples.

Contribution

The paper presents a novel combination of variational iteration and homotopy perturbation methods to solve high-order boundary value problems.

Findings

Rapid convergence of the series solutions

Effective handling of seventh order boundary value problems

Numerical examples confirm efficiency and accuracy

Abstract

The induction motor behaviour is represented by a fifth order differential equation model. Addition of a torque correction factor to the model accurately reproduces the transient torques and instantaneous real and reactive power flows of the full seventh order differential equation model. The variational iteration homotopy perturbation method (VIHPM) is employed to solve the seventh order boundary value problems. The approximate solutions of the problems are obtained in terms of a rapidly convergent series. Several numerical examples are given to illustrate the implementation and efficiency of the method.