具有延迟和Neumann边界条件的超扩散型空间分数阶方程组的数值方法

IF 0.3 Q4 MATHEMATICS
M. Ibrahim, V. Pimenov
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引用次数: 0

摘要

考虑具有泛函一般时滞和Neumann边界条件的两个空间分数超扩散方程系统。对于这个问题,基于移位的gr nwald- letnikov公式来近似分数阶Riesz导数,并使用离散史前的分段线性插值和延拓外推来考虑延迟效应,构造了一种类似的Crank-Nicolson方法。利用Gershgorin定理,证明了差分格式的可解性及其稳定性。得到了该方法的收敛阶数。给出了数值实验结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical method for system of space-fractional equations of superdiffusion type with delay and Neumann boundary conditions
We consider a system of two space-fractional superdiffusion equations with functional general delay and Neumann boundary conditions. For this problem, an analogue of the Crank-Nicolson method is constructed, based on the shifted Grünwald-Letnikov formulas for approximating fractional Riesz derivatives with respect to a spatial variable and using piecewise linear interpolation of discrete prehistory with extrapolation by continuation to take into account the delay effect. With the help of the Gershgorin theorem, the solvability of the difference scheme and its stability are proved. The order of convergence of the method is obtained. The results of numerical experiments are presented.
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