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Finite difference methods and their physical constraints for the fractional Klein-Kramers equation. (English) Zbl 1233.65052
The authors present a finite difference scheme for solving the fractional Klein-Kramers differential equation, that is obtained based on incorporating subdiffusive mechanisms into the Klein-Kramers formalism. The stability of the numerical scheme is analyzed, and a condition for stability is obtained which indicates the ratio between the kinetic energy of the particle and temperature of the fluid can not be too large. Numerical results coincide the theoretical results on rate of convergence and confirm the effectiveness of the present scheme.

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
35Q35 PDEs in connection with fluid mechanics
35R11 Fractional partial differential equations
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