标题： 分数次扩散方程的指数B样条配置方法 显示英文标题

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

摘要： 在本文中，我们提出了一种指数B样条配点方法来近似Caputo型分数次扩散方程的解。 目前的方法是通过在时间上使用Gorenflo-Mainardi-Moretti-Paradisi（GMMP）方案和在空间上使用高效的基于指数B样条的方法生成的。 唯一可解性得到了严格的讨论。 其稳定性通过一个与经典von Neumann方法密切相似的程序得到了很好的说明。 得到的代数系统是三对角的，可以通过已知的代数求解器快速求解，成本低且存储需求小。 最后进行了一系列数值实验，并与其他文献中可用的算法进行对比，数值结果证实了我们方法的有效性和优越性。 显示英文摘要

摘要： In this article, we propose an exponential B-spline collocation method to approximate the solution of the fractional sub-diffusion equation of Caputo type. The present method is generated by use of the Gorenflo-Mainardi-Moretti-Paradisi (GMMP) scheme in time and an efficient exponential B-spline based method in space. The unique solvability is rigorously discussed. Its stability is well illustrated via a procedure closely resembling the classic von Neumann approach. The resulting algebraic system is tri-diagonal that can rapidly be solved by the known algebraic solver with low cost and storage. A series of numerical examples are finally carried out and by contrast to the other algorithms available in the literature, numerical results confirm the validity and superiority of our method.