Backward substitution method based on Müntz polynomials for solving the nonlinear space fractional partial differential equations

A computational technique based on the Müntz polynomials and meshless method has been presented for the solution of nonlinear and linear space fractional partial differential equations (PDEs). The meshless method that is used in this study is the new version of backward substitution method (BSM). First, the time‐derivative term is discretized by the Crank‐Nicolson method. Then, the approximate solution is given as the separation of the approximation of the boundary data and the correcting functions using the Müntz polynomials. In general form, this approximate solution that does not necessarily satisfy the original equation is shown as the sum of the system basics in which it consists free parameters. Finally, these parameters are determined by the BSM method inside the domain. The main advantage of the method is efficiency and reliability that is examined by six numerical experiments.