Application of He’s homotopy perturbation method to Volterra’s integro-differential equation. (English) Zbl 1401.65150

El-Shahed, Moustafa

Int. J. Nonlinear Sci. Numer. Simul. 6, No. 2, 163-168 (2005).

Summary: In this paper, He’s Homotopy Perturbation Method is proposed for solving Volterra’s Integro-differential Equation. The Volterra’s population model is converted to a nonlinear ordinary differential equation and the solution of which is then approximated by using the differential transform method. He’s homotopy perturbation method is implemented to the model and the solution is obtained. The results reveal that the method is very effective and convenient.

MSC:

65R20	Numerical methods for integral equations
45D05	Volterra integral equations
65L99	Numerical methods for ordinary differential equations
34K07	Theoretical approximation of solutions to functional-differential equations
45J05	Integro-ordinary differential equations

Keywords:

Volterra’s population model; differential transform; integro-differential equations; homotopy perturbation method; Pade’s approximation