时间分数阶扩散方程的新型耦合格式
首发时间:2019-04-11
摘要:本文构造了一种求解时间分数阶扩散方程的新型耦合格式。由于时间分数阶扩散方程的解在t=0附近通常具有奇异性,基于一致时间步长的L1离散格式并不能达到理想收敛阶。通过对初始时刻附近的解采用渐近逼近,而其它时间区域的解运用基于非一致时间步长的L1公式进行模拟,本文构造了一种求解时间分数阶扩散方程的新型耦合格式。数值结果表明,新格式不仅能达到理想的收敛阶,而且当分数阶导数减小,解的奇异性增强时,也能取得较经典格式更优的计算结果。
关键词: 时间分数阶扩散方程 奇异性 非一致时间步长 渐近逼近
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New coupling scheme for the time fractional diffusion equation
Abstract:In this paper, we study a new coupling scheme for the time fractional diffusion equation. Since the solution of the given problem usually has a singularity near the initial time, the discrete methond which consist of L1 formula based on a uniform mesh in time can not reach the ideal convergence rate. By using the asymptotic solution near the initial time, and applying L1 formula based on a nonuniform mesh in the other, a new coupling scheme for the time fractional diffusion equations is proposed. Numerical results show that the new scheme can reach the ideal convergence order in time. And as the fractional derivative decreases, the singularity near the initial time increases, the new method has much better results than that of the classical one.
Keywords: Time fractional diffusion equation Singularity Nonuniform mesh Asymptotic approximation
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