A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

Abstract

In this paper, we develop and analyze a high order compact finite difference method (CFDM) for solving a general class of two-point nonlinear singular boundary value problems with Neumann and Robin boundary conditions arising in various physical models. Convergence result of this method is established through matrix analysis approach. To illustrate the applicability and accuracy of the method, we consider nine numerical examples, including heat conduction in the human head, equilibrium of isothermal gas sphere, oxygen-diffusion in a spherical cell and reaction–diffusion process in a spherical permeable catalyst. It is shown that the computational order of convergence of the proposed CFDM is four. The obtained results are compared with those obtained by other existing numerical methods.