A numerical Scheme for Fractional Partial Differential Equations Based on Green-CAS Function and CAS wavelets

Abstract

This study manifests to acquire a numerical scheme to detect the numerical solutions of partial differential equations of arbitrary order subject to the initial and boundary condition. This novel approach comprises of a Green function and CAS wavelets named Green-CAS technique. The present approach is not only simple and easy to implement due to Green function but it also vanishes the operational matrices for boundary conditions. While tackling the nonlinear partial differential equations of arbitrary order, the Picard technique is used to linearize system, and then the Green- CAS approach is implemented. Moreover, the order of convergence for two parameters has been also demonstrated in convergence analysis that assembles the proposed technique more strengthens. To show validity of the recommended technique, the acquired outcomes are compared with the CAS wavelets and other various renowned techniques. In addition, results of various applications express in the form of graphics and tables which elaborate the effectiveness and correctness of the discussed method.