Third(fourth) order accurate method for one dimensional local fractional Viscous Burgers’ and diffusion-convection equations

Abstract

A Singular fractal boundary value problem whose order term is a Hausdroff Fractal derivative of order δ ∈ (0, 1] is considered. In this article, using three grid points, we discuss the variable mesh method of order three that requires only three function evaluations on some regularity conditions. we give importance to solve a singular problem in our scheme and prove that the recommended scheme is significant. We also discussed the convergence analysis of our method and proved that the method is reliable, like classical numerical methods. Special numerical illustrations for solving linear and nonlinear fractal differential equations are provided to demonstrate the accurate outcome of the recommended method, which has been discussed in convergence analysis.