A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions |
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Authors: | Xuan Zhao Zhi-zhong Sun |
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Institution: | Department of Mathematics, Southeast University, Nanjing 210096, PR China |
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Abstract: | Combining order reduction approach and L1 discretization, a box-type scheme is presented for solving a class of fractional sub-diffusion equation with Neumann boundary conditions. A new inner product and corresponding norm with a Sobolev embedding inequality are introduced. A novel technique is applied in the proof of both stability and convergence. The global convergence order in maximum norm is O(τ2−α + h2). The accuracy and efficiency of the scheme are checked by two numerical tests. |
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Keywords: | Neumann boundary conditions Sub-diffusion equation Box-type scheme Stability Convergence Energy method |
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