A finite difference/finite element technique with error estimate for space fractional tempered diffusion-wave equation. (15th April 2018)

• Record Type: Journal Article
• Authors: Dehghan, Mehdi; Abbaszadeh, Mostafa
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 8(2018)
• Page Start: 2903
• Page End: 2914
• Publication Date: 2018-04-15
• Subjects: Space fractional equation -- Tempered fractional diffusion-wave equation -- Convergence analysis -- Error estimate -- Riemann–Liouville fractional -- Finite element method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.01.020
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: An efficient numerical technique is proposed to solve one- and two-dimensional space fractional tempered fractional diffusion-wave equations. The space fractional is based on the Riemann–Liouville fractional derivative. At first, the temporal direction is discretized using a second-order accurate difference scheme. Then a classic Galerkin finite element is employed to obtain a full-discrete scheme. Furthermore, for the time-discrete and the full-discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed numerical method. Finally, two test problems have been illustrated to verify the efficiency and simplicity of the proposed technique.