A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions

Abstract

We proposed a Least Squares Finite Element Method (LSFEM) for the approximate solution of Time fractional telegraph equation (TFTE). The method implemented the Vieta-Lucas polynomials expressed in the Caputo fractional sense as basis functions. The LSFEM reduces the TFTE into algebraic system with element matrices and vectors, while the Conjugate Gradient Method (CGM) solved the system for the unknowns with the aid of MAPLE 18. The results generated implies that the proposed method converges favorably to the theoretical solution when the number of elements is large with a large space-time step used for the parameter t.

Keywords

• Telegraph equation
• Conjugate gradient method
• Finite element method
• Orthogonal polynomials
• Vieta-Lucas polynomials
• Fractional calculus