Multipoint Boundary Problems for Integral - Differential Equations Solved by Homotopy Perturbation Method

摘要

This paper proposes an algorithm based on the homotopy perturbation method (HPM) for the solving the one-dimensional neutron transport equation with suitable multipoint boundary conditions (MPBC). The homotopy perturbation method is a coupling of traditional perturbation method and the homotopy function from topology, which continuously deforms the given problem to another that can be easily solved. The new version of homotopy method, upon which our algorithm is built, yields rapid convergence of the solution series to exact solution. Usually only two iterations lead to high accuracy solutions. Illustrative numerical examples are provided to prove the efficiency of the proposed algorithm for integral differential equations accompanied by the multipoint boundary conditions.