Abstract
In this paper, a new numerical algorithm for solving the time fractional convection–diffusion equation with variable coefficients is proposed. The time fractional derivative is estimated using the L_{1} formula, and the spatial derivative is discretized by the sinc-Galerkin method. The convergence analysis of this method is investigated in detail. The numerical solution is 2-alpha order accuracy in time and exponential rate of convergence in space. Finally, some numerical examples are given to show the effectiveness of the numerical scheme.
Highlights
1 Introduction In the last few decades, fractional differential equations have been widely applied in various fields of science and engineering to model many phenomena [1,2,3,4,5,6,7,8,9,10,11]
In [38], a new reliable algorithm based on the sinc function is employed for the time fractional diffusion equation
4 Convergence analysis we show that the approximate solution unM(x) converges to the exact solution un(x) of (12) at an exponential rate
Summary
In the last few decades, fractional differential equations have been widely applied in various fields of science and engineering to model many phenomena [1,2,3,4,5,6,7,8,9,10,11]. We consider the following time fractional convection–diffusion equation with variable coefficients:. In [34], Nagy applied the sinc-Chebyshev collocation method for numerical investigation of the time fractional nonlinear Klein–Gordon equation. In [35], Saadatmandi et al proposed the sinc-Legendre collocation method for a class of fractional convection–diffusion equations with variable coefficients. In [38], a new reliable algorithm based on the sinc function is employed for the time fractional diffusion equation. In [39], Jalilian et al adopted an algorithm based on sinc basis functions for the numerical solution of the nonlinear fractional integro-differential equation of pantograph type. We apply the sinc-Galerkin method to solve the time fractional convection–diffusion equation with variable coefficients.
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