Solving time-fractional differential diffusion equation by theta-method. (English) Zbl 1359.65147

Aslefallah, Mohammad; Rostamy, Davood; Hosseinkhani, Khadijeh

Int. J. Adv. Appl. Math. Mech. 2, No. 1, 1-8 (2014).

Summary: This paper proposes a numerical method to deal with the one-dimensional time-fractional diffusion equation defined by Caputo fractional derivative. The paper aims to present a general framework of the \(\theta\)-method for solving time-fractional diffusion differential equations for \((0 \leq \theta \leq 1)\). Consistency, stability and convergence analysis of the method is discussed. Finally, the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R11	Fractional partial differential equations

Keywords:

fractional PDE (FPDE); finite differences \(\theta\)-method; Caputo fractional derivative; von-Neumann stability analysis