In this paper,we will study the time fractional convection-diffusion equation with variable coefficients.First,we use the finite difference method.The time variable is discretized,and the semi-discrete scheme of the equation is obtained.The exact solution u(x,tn)of the equation is obtained by using the theory of reproducing kernel method.Then the exact solution u(x,tn)is truncated by m term to obtain the approximate solution um(x,tn).By proving,we know that the method is stable.Moreover,u(i)m(x,tn)converge uniformly to u(i)(x,tn)(i=0,1,2).Finally,we give several numerical examples and compare them with the methods in other literatures,which show that our algorithm is effective.
维普
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