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An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time
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In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval (0, 1). An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.
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Caputo derivative fractional differential equation subdiffusion finite difference method distributed order differential equation FRACTIONAL SUB-DIFFUSION SUBDIFFUSION EQUATION STABILITY SCHEME