A finite difference/finite element technique with error estimate for space fractional tempered diffusion-wave equation. (English) Zbl 1415.65224
Summary: 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.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin 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 |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
space fractional equation; tempered fractional diffusion-wave equation; convergence analysis; error estimate; Riemann-Liouville fractional; finite element methodSoftware:
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