Abstract
A Crank-Nicolson numerical approximation on graded meshes for time fractional mixed diffusion and wave equation with two Caputo derivatives of fractional order: one belonging to (0, 1), the other belonging to (1, 2), is established and analyzed. We derive Crank-Nicolson formulae to approximate fractional operators, which can obtain second-order accuracy. Error estimates are analyzed strictly. The main contribution of this paper is to show that the Crank-Nicolson numerical approximation for the model problem under consideration is temporal second-order accurate over graded meshes. Numerical tests are presented to support our theoretical results.KeywordsTime fractional mixed diffusion and wave equation with an initial singularityCrank-Nicolson formulaError estimate
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