The use of variational iteration method and homotopy perturbation method for solving two nonlinear equations

Abstract

PurposeThe purpose of this paper is to implement variational iteration method (VIM) and homotopy perturbation method (HPM) to solve modified Camassa‐Holm (mCH) and modified Degasperis‐Procesi (mDP) equations.Design/methodology/approachPerturbation method is a traditional method depending on a small parameter which is difficult to be found for real‐life nonlinear problems. To overcome the difficulties and limitations of the above method, two new ones have recently been introduced by He, i.e. VIM and HPM. In this paper, mCH and mDP equations are solved through these methods.FindingsTo assess the accuracy of the solutions, the comparison of the obtained results with the exact solutions reveals that both methods are tremendously effective.Originality/valueThe paper shows that VIM and HPM can be implemented to solve mCH and mDP equations.