A high order numerical method for the variable order time-fractional reaction-subdiffusion equation. (English) Zbl 07846792
Summary: In this paper, we present a high order new numerical approximation for variable order Caputo fractional derivative of order \(0 < \alpha(\mathrm{x}, t) < 1\), by using the idea of interpolation. Then, by using this approximation, a numerical scheme is presented by using finite difference approach for variable order time fractional reaction-subdiffusion equation (VO-TFRSDE). The unconditionally stability of the numerical scheme is examined theoretically. The scheme is implemented on the two test problems. The numerical results are highly accurate with higher order of convergence.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 26Axx | Functions of one variable |
| 35Kxx | Parabolic equations and parabolic systems |
Keywords:
variable order Caputo derivative (VOCD); variable order reaction-subdiffusion equation; L-123 approximation; stability analysisReferences:
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