Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations

We consider one-dimensional fractional sub-diffusion equations on an unbounded domain. For a problem of this type for which an exact or approximate artificial boundary condition is available we reduce it to an initial-boundary value problem on a bounded domain. We then analyze the numerical solution of the problem by polynomial and nonpolynomial spline methods. The consistency and the Von Neumann stability analysis of these methods are also discussed. Numerical experiments clarify the effectiveness and order of accuracy of the proposed methods.