A mixed decomposition-spline approach for the numerical solution of a class of singular boundary value problems

In this paper, we formulate a patching scheme to solve numerically a class of boundary value problems. The strategy is being founded on a merger of two methods, a modified decomposition technique applied on a small interval near the singularity and a fourth order spline collocation technique which is used on the rest of the domain of the problem. The convergence of the proposed method is analyzed and a fourth-order rate of convergence is proved. Some examples are given to test the efficiency of the scheme and to verify the order of the rate of convergence. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods.