Approximate Solutions of Some Linear Boundary Value Problems Using the Homotopy Analysis Method Combined with Sumudu Transform

This paper considers a combined form of the Sumudu transform with the modified homotopy analysis method (MHAM) to find approximate and analytical solutions for linear two-point boundary value problems. This method is called the modified Sumudu transform homotopy analysis method (MSTHAM). The suggested technique relies on the freedom of the homotopy analysis method (HAM) by introducing an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHAM will be required, as compared to STHAM, which needs more iterations for the same cases of study. The proposed method has been applied to solve two examples and the results have been compared with those obtained by the standard STHAM and the exact solutions, where it is found that the proposed solutions are of high accuracy and, therefore, MSTHAM is extremely efficient, simple and can be applied to other types of problems.