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The approximate solutions of time-fractional diffusion equation by using Crank-Nicolson method. (English) Zbl 1349.65274

Summary: We consider approximate solution of time-fractional diffusion equation (TFDE) by using Crank-Nicolson method. Besides, we utilize property of Riemann-Liouville derivative to obtain this solution. Then, we draw three dimensional graphics of this solution by means of programming language Mapple. Finally, we show table including error \(\alpha\), \(x\), \(t\), \(M\) and \(N\). Numerical results ensure to illustrate the effectiveness and reliability of this method.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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