Authors : A.F. Jameel, A. Saaban, H. Akhadkulov and F.M. Alipiah
Abstract: This study discusses the approximate solution of nonlinear Volterra Hammerstein Integral Equations (VHIEs) using Homotopy Perturbation Method (HPM). Based on the previous literature, the use of HPM for solving VHIEs are very limited. Most of them focus toward the solving of Fredholm and Volterra integro-differential equations. In this proposed method, homotopy are constructed in the form Ly+p(Ny+Ny-Ly) = 0 where L, N are linear operator p∈[0, 1] is an embedding parameter to generate approximate series solution converge to the exact solution of VHIEs. We implement our proposed by using two specific examples of VHIEs.
A.F. Jameel, A. Saaban, H. Akhadkulov and F.M. Alipiah, 2019. Homotopy Perturbation Method (HPM) for Solving Nonlinear Volterra Hammerstein Integral Equations. Journal of Engineering and Applied Sciences, 14: 5598-5601.