Non-polynomial fractal quintic spline method for nonlinear boundary-value problems

Abstract

In this study, we have proposed second, fourth and sixth order convergent numerical techniques for approximating linear and non-linear boundary value problems of second order with the help of fractal non-polynomial spline function. We have discussed the convergence analysis and error bound for sixth order method to prove the theoretical aspects of the presented method. Numerical problems are experimented to validate the theoretical results. Comparison with fractal polynomial and few other existing methods leads us to the conclusion that the proposed technique is more efficient.