Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations

Herein, we propose a numerical scheme to solve spectrally hyperbolic partial differential equations (HPDEs) using Galerkin method and approximate the solutions using double shifted Jacobi Polynomials. The main characteristic behind this approach is that it reduces such problems to those of solving systems of algebraic equations which greatly simplifies the problem. The validity and efficiency of the proposed method are investigated and verified through several examples. (C) 2019 Elsevier Ltd. All rights reserved.