A High-Order Difference Scheme for the Generalized Cattaneo Equation

Abstract

A high-order finite difference scheme for the fractional Cattaneo equation is investigated. The $L_1$ approximation is invoked for the time fractional part, and a compact difference scheme is applied to approximate the second-order space derivative. The stability and convergence rate are discussed in the maximum norm by the energy method. Numerical examples are provided to verify the effectiveness and accuracy of the proposed difference scheme.