当前位置: X-MOL 学术J. Sci. Comput. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Generalized Exponential Time Differencing Schemes for Stiff Fractional Systems with Nonsmooth Source Term
Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2021-01-07 , DOI: 10.1007/s10915-020-01374-y
Ibrahim O. Sarumi , Khaled M. Furati , Abdul Q. M. Khaliq , Kassem Mustapha

Many processes in science and engineering are described by fractional systems which may in general be stiff and involve a nonsmooth source term. In this paper, we develop robust first, second, and third order accurate exponential time differencing schemes for solving such systems. Rather than imposing regularity requirements on the solution to account for the singularity caused by the fractional derivative, we only consider regularity requirements on the source term for preserving the optimal order of accuracy of the proposed schemes. Optimal convergence rates are proved for both smooth and nonsmooth source terms using uniform and graded meshes, respectively. For efficient implementation, high-order global Padé approximations together with their fractional decompositions are developed for Mittag–Leffler functions. We present numerical experiments involving a typical stiff system, a fractional two-compartment pharmacokinetics model, a two-term fractional Kelvin–Viogt model of viscoelasticity, and a large system obtained by spatial discretization of a sub-diffusion problem. Demonstrations of the efficiency of the rational approximation implementation technique and the newly constructed high-order schemes are provided.



中文翻译:

具有非光滑源项的刚性分数阶系统的广义指数时差方案

分数系统描述了科学和工程学中的许多过程,分数系统通常可能是僵化的,并且涉及不平滑的源术语。在本文中,我们开发了用于解决此类系统的鲁棒的一阶,二阶和三阶精确指数时间差分方案。我们没有在解决方案上强加规则性要求以解决分数导数引起的奇异性,而是只考虑了源项的规则性要求,以保持所提出方案的最佳精度。分别使用均匀和渐变网格证明了平滑和非平滑源项的最优收敛速度。为了有效实施,针对Mittag–Leffler函数开发了高阶全局Padé逼近及其分数分解。我们提供的数值实验涉及典型的刚性系统,分数两室药代动力学模型,粘弹性的二项分数Kelvin-Viogt模型和通过子扩散问题的空间离散化获得的大型系统。提供了有理逼近实现技术和新构建的高阶方案效率的证明。

更新日期:2021-01-07
down
wechat
bug