High order numerical method for a subdiffusion problem

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Carla Jesus, Ercília Sousa
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引用次数: 0

Abstract

We consider a subdiffusive fractional differential problem characterized by an equation that incorporates a time Riemann-Liouville fractional derivative of order 1α, α(0,1), on its right-hand side, while the diffusive coefficient is allowed to vary with both space and time. An high order numerical method for the subdiffusion problem is derived based on the fractional splines of degree β(1,2]. The main purpose of this work is to apply fractional splines for approximating the fractional integral in the definition of the Riemann-Liouville fractional derivative, and hence explain how to solve the subdiffusion problem using this approach. It is discussed how the rate of convergence of the numerical method depends on the solution, the degree of the spline and the order of the fractional derivative.

亚扩散问题的高阶数值方法
我们考虑了一个亚扩散分式微分问题,其特征是方程的右边包含阶数为 1-α 的时间黎曼-刘维尔分式导数 α∈(0,1),同时允许扩散系数随空间和时间变化。基于度数为 β∈(1,2]的分数样条,推导出了亚扩散问题的高阶数值方法。这项工作的主要目的是应用分数样条逼近黎曼-刘维尔分数导数定义中的分数积分,从而解释如何利用这种方法求解亚扩散问题。文中讨论了数值方法的收敛速度如何取决于解、样条线的阶数和分数导数的阶数。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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