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

Abstract

Abstract 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.

Keywords

• fractional sub-diffusion equation
• exponential B-spline collocation method
• unique solvability
• unconditional stability