Efficient Numerical Method For A Time Fractional Dual-phase Lag Heat Transfer Equation

Recently,the time fractional dual-phase lag(DPL)heat transfer equation has become an important class of heat transfer models.The main aim of this paper is to develop efficient numerical method for the time fractional DPL heat transfer equation.First we discuss the priori estimates of the solution involving the homogeneous and inhomogeneous time fractional DPL heat transfer equation.Then we establish the semi-discrete and fully discrete numerical schemes for the considered problem based on the backward Euler convolution quadrature in time and the finite element method in space.To improve the devised fully discrete scheme,a fast numerical algorithm is proposed to reduce the computational cost and memory.For these developed numerical methods,the error estimates are investigated rigorously.Comparing with the existing numerical methods for the time fractional DPL heat transfer model,a significant advantage of the present work is that its error analysis is based on the regularity of the initial value and the right hand function instead of the assumption of smooth exact solution.Finally,numerical examples are presented to confirm the theoretical results and the effectiveness of numerical schemes.