Modified homotopy perturbation method for integro-differential and hypersingular integral equations - Zulkarnain, Fatimah Samihah (2018)
Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHPM) are obtained in the class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D) where D is a closed subspace of R2 for higher order FVIDE problem. Many researchers solved singular integral equation with kernel equal to one. This study describes the implementation of HPM and MHPM on HSIE of the first kind with kernel is a constant on a diagonal. Convergence and error estimation are obtained in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second kind. For all cases, numerical examples are provided to exhibit the efficiency of the methods. The results obtained are more accurate than the previous works.