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A second-order difference scheme for two-dimensional two-sided space distributed-order fractional diffusion equations with variable coefficients
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A second-order difference scheme for two-dimensional two-sided space distributed-order fractional diffusion equations with variable coefficients
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A second-order difference scheme for two-dimensional two-sided space distributed-order fractional diffusion equations with variable coefficients
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Journal Article
A second-order difference scheme for two-dimensional two-sided space distributed-order fractional diffusion equations with variable coefficients
2024
Overview
In this paper, a second-order difference scheme is developed to solve two-dimensional two-sided space distributed-order fractional diffusion equation with variable coefficients. In the spatial direction, a second-order difference scheme is proposed, the distribution-order integral is discretized by the Gauss–Legendre quadrature formula and the space fractional derivative is approximated by the weighted and shifted Grünwald–Letnikov operators. In addition, the time direction is discretized into a second-order difference scheme by the Crank–Nicolson method. Therefore, the main numerical scheme is developed. Furthermore, a small perturbation is added to the main difference scheme to construct an alternating-direction implicit scheme. Also, the stability and convergence of the numerical scheme are proved. Finally, some numerical results are provided to show the accuracy and efficiency of the proposed method.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
