Doubly singular boundary value problems with derivative dependent source function: A fast-converging iterative approach

摘要

In this paper, a fast-converging recursive scheme is presented to approximate the solution of a class of derivative dependent doubly singular boundary value problems (DDSBVP). First, the original problem is reformulated as an equivalent integral equation. The resulting integral equation is then efficiently tackled by an improved homotopy analysis method (IHAM). This method contains a parameter, which greatly accelerates the convergence of the series solution. The convergence of the method is carried out. To illustrate the efficiency and accuracy of the proposed recursive approach, we consider three nonlinear examples, including one physical model problem, which describes stress distribution on a rotationally shallow membrane cap. Results show that our method excels over the existing methods.