Spline in tension method for non-linear two point boundary value problems on a geometric mesh

In this paper, we discuss a new method based on spline in tension approximation for the numerical solution of two-point non-linear boundary value problems on uniform mesh. The method is of order four. We have discussed the derivation and the convergence of the proposed method in detail. The method is extended to non-uniform mesh. Numerical results are given to illustrate the efficiency of the proposed method.