A new efficient recursive technique for solving singular boundary value problems arising in various physical models

Abstract

The paper deals with a numerical technique for solving nonlinear singular boundary value problems arising in various physical models. First, we convert the original problem to an equivalent integral equation to surmount the singularity and employ afterward the boundary condition to compute the undetermined coefficient. Finally, the integral equation without undetermined coefficient is treated using homotopy perturbation method. The present method is implemented on three physical model examples: i) thermal explosions; ii) steady-state oxygen diffusion in a spherical shell; iii) the equilibrium of the isothermal gas sphere. The results obtained by the present method are compared with that obtained using finite-difference method, B-spline method and a numerical technique based on the direct integration method, and comparison reveals that the proposed method with few solution components produces similar results and the method is computationally efficient than others.