2016/07/24 by Zhu, X. G., Nie, Y. F., Yuan, Z. B. +2
#35R11(Secondary) #65M70(Primary) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1607.07436
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.