A novel approach based on mixed exponential compact finite difference and OHA methods for solving a class of nonlinear singular boundary value problems

This work aims to find the numerical solution to a class of nonlinear singular boundary value problems (SBVPs). The considered problem has a singularity at x = 0. We introduce a computational technique comprising an optimal homotopy analysis (OHA) approach and exponential compact finite difference method (ECFDM) to solve this SBVPs. In this technique, the domain of the problem I=[0,1] is divided into two subintervals as I=I1∪I2=[0,ξ]∪[ξ,1] (the point x=ξ is chosen sufficiently close to the singularity). In interval I1, we employ the OHA scheme to overcome the singularity. In interval I2, an ECFDM is designed to solve the resultant boundary value problem (BVP). Convergence analysis of the ECFDM is discussed. Furthermore, numerical experiments are performed to confirm the theoretical claims. The proposed ECFDM is shown to be fourth-order convergence.