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A compact finite difference scheme for the fractional sub-diffusion equations. (English) Zbl 1211.65112
Authors’ abstract: A compact finite difference scheme for the fractional sub-diffusion equations is derived. After a transformation of the original problem, the L1 discretization is applied for the time-fractional part and a fourth-order accuracy compact approximation for the second-order space derivative. The unique solvability of the difference solution is discussed. The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis. The technique is quite novel and different from previous analytical methods. Finally, a numerical example is provided to show the effectiveness and accuracy of the method.
MSC:
65M06Finite difference methods (IVP of PDE)
35K05Heat equation
35R11Fractional partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
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