Non-polynomial spline method for solving Bratu's problem

Smooth approximate solutions of the one-dimensional Bratu's problem are developed by using non-polynomial spline function. The inverse of some tridiagonal matrices are obtained which are required in proving the convergence analysis of the presented method. By considering the maximum absolute errors in the solution at grid points and tabulated in tables for different choices of step size we conclude that our presented method produces more accurate results in comparison with those obtained by B-spline, Laplace and decomposition methods.