A compact finite difference method for solving a class of time fractional convection-subdiffusion equations (Q906962)

The paper deals with the numerical solution of time fractional convection-subdiffusion equations with the aid of a high-order compact finite difference method. The convection coefficient in the equation may be spatially variable, and the time fractional derivative is in Caputo's sense with the order \(\alpha\) (\(0<\alpha<1\)). After a transformation of the original equation, the spatial derivative is discretized by a fourth-order compact finite difference method and the time fractional derivative is approximated by a \((2-\alpha)\)-order implicit scheme. The local truncation error and the solvability of the method are discussed in detail. A rigorous theoretical analysis of the stability and convergence is carried out using the discrete energy method, and the optimal a priori error estimates in the discrete \(H^1\), \(L^2\) and \(L^\infty\) norms are obtained. Three numerical examples, with known exact solutions, demonstrate the orders of convergence of the proposed method.