期刊
NONLINEAR DYNAMICS
卷 97, 期 4, 页码 2757-2775出版社
SPRINGER
DOI: 10.1007/s11071-019-05160-w
关键词
Riemann-Liouville fractional derivative; Modified anomalous sub-diffusion model; RBF-FD; Stability; Convergence
The nonlinear modified anomalous sub-diffusion model characterizes processes that become less anomalous as time progresses by including a second fractional time derivative acting on the term of diffusion. This paper introduces a radial basis function-generated finite difference (RBF-FD) method for solving the governing problem. The Grunwald-Letnikov formula with first-order accuracy is implemented to discretize the problem in the time direction, and the spatial variable is discretized using the local RBF-FD method. The convergence and stability of the time discretization scheme are deduced in an appropriate Sobolev space. The data distribution pattern within the support domain is considered to have a constant number of points. The numerical results on regular and irregular domains show the efficiency and high accuracy of the method and confirm the theoretical prediction.
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