An iterative technique for solving a class of local and nonlocal elliptic boundary value problems

Abstract

An optimal iterative method is proposed for a reliable solution of a class of Bratu-type, Troesch’s and nonlocal elliptic boundary value problems (BVPs). Due to the presence of parameter $$\delta $$ as well as strong nonlinearity, these problems pose difficulties in obtaining their solutions. With the help of Green’s function theory, we first transform the BVP into an equivalent integral equation, followed by applying the optimal homotopy analysis method to get the approximate solution of high accuracy level. Several examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The numerical results confirm the reliability of the present method as it tackles such nonlocal problems without any limiting assumptions. The convergence and error analysis of the proposed method is discussed.