Syed Tauseef Mohyud‐Din, Ahmet Yıldırım and Sefa Anıl Sezer
The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are…
Abstract
Purpose
The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are calculated in the form of a convergent power series with easily computable components.
Design/methodology/approach
The HPM is used to obtain numerical soliton solution of the IBE. The solutions are calculated in the form of a convergent power series with easily computable components.
Findings
The errors are obtained by using the approximate solution given by using only two iterations of the HPM. It is evident that the efficiency of this approach can be dramatically enhanced by computing further terms of approximate solution.
Originality/value
The numerical results presented in the paper show that only a few terms are sufficient to obtain accurate solutions.
Details
Keywords
Sefa Anıl Sezer, Ahmet Yıldırım and Syed Tauseef Mohyud‐Din
The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer‐order differential equation, to derive explicit and numerical…
Abstract
Purpose
The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer‐order differential equation, to derive explicit and numerical solutions of the fractional KdV‐Burgers‐Kuramoto equation.
Design/methodology/approach
The authors used Maple Package to calculate the functions obtained from the HPM.
Findings
The fractional derivatives are described in the Caputo sense. HPM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.
Originality/value
The paper describes how the HPM has been successfully applied to find the solution of fractional KdV‐Burgers‐Kuramoto equation.