Cubic spline based differential quadrature method: A numerical approach for fractional Burger equation

Abstract

In this research paper, our main objective is to represent a direct numerical approach for solving time-fractional Burger's equation using modified hybrid B-spline basis function. The Caputo derivative is used to discretize the time-fractional derivative and for Space derivative Differential Quadrature Method (DQM) based on B-Spline is used. The DQM method has its own inherited advantage being a simple and programable method. The embedding of B-spline basis makes it more practical to approximate the solution curve. DQM with B-spline basis is a simple and efficient technique based on the matrix approach. The problem is discretized in the system of nonlinear equations and then further solved by a programming tools. The stability is examined by the matrix-based approach. The presented method has been applied to three test problems. The obtained results showed that the proposed method is good for solving non-linear time-fractional Burger's equation. The approximated solutions are graphically represented and the results showed that solutions are closed to the exact solution.