An exponential B-spline collocation method for the fractional sub-diffusion equation

Advances in Difference Equations

Zhanbin Yuan¹  Zongze Yang¹  Xiaogang Zhu¹  Yufeng Nie²  Jungang Wang² 

[1] Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, P.R. China

关键词: fractional sub-diffusion equation;    exponential B-spline collocation method;    unique solvability;    unconditional stability;   

DOI  :  10.1186/s13662-017-1328-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we propose an exponential B-spline approach to obtain approximate solutions for the fractional sub-diffusion equation of Caputo type. The presented method is established via a uniform nodal collocation strategy by using an exponential B-spline based interpolation in conjunction with an effective finite difference scheme in time. The unique solvability is rigorously proved. The unconditional stability is well illustrated via a procedure closely resembling the classic von Neumann technique. A series of numerical examples are carried out, and by contrast to other algorithms available in the open literature, numerical results confirm the validity and superiority of our method.

【 授权许可】

CC BY