时间-分数阶四阶反应-扩散模型的数值格式

Dilara Altan Koç
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引用次数: 0

摘要

. 在分数阶微积分中,分数阶微分方程在物理上和理论上都很重要。本文开发了一种有效的数值处理方法。采用有限差分隐式方法,通过增加迭代次数,得到了时间分数阶四阶反应扩散方程在Caputo导数意义下的数值解。隐式差分格式的优点是无条件稳定。对算法的稳定性分析和收敛性进行了验证。给出了一个数值算例,并用表格和图形证明了该方法的有效性
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A numerical scheme for time-fractional fourth-order reaction-diffusion model
. In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics
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CiteScore
2.00
自引率
10.00%
发文量
30
审稿时长
25 weeks
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