An innovative pseudo-spectral Galerkin algorithm for the time-fractional Tricomi-type equation

Abstract

Abstract Herein, we offer semi−analytic numerical procedures for the 1−D Tricomi−type time−fractional equation (T−FTTE). We consider the Jacobi−shifted polynomials as basis functions (BFs). A novel spectral approach is implemented based on the Galerkin procedure to tackle the Tricomi−type equation. The main strength of this approach is, it reduces the diverseial problem into solving an algebraic system of equations. The constructed methodology is successfully extended to solve the 2−D T−FTTE. Some numerical test experiments are exhibited to verify the proficiency and high accuracy of the proposed method.