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• W3041795894 abstract "Abstract The fractional Klein-Kramers equation describes the process of subdiffusion in the presence of an external force field in phase space and incorporates a fractional operator in time of order α, 0  2 − α . It is proved, for the open domain, that the schemes satisfy the positivity preserving property. The positivity preserving property for the explicit schemes imposes a strong condition in the relation between time step, space step and phase step, for small values of α, highlighting the advantage of using implicit schemes in these cases. For a bounded domain in space, two types of boundary conditions are considered, absorbing boundary conditions and reflecting boundary conditions. The inclusion of boundary conditions leads to some technical complications that require changes in the schemes near the boundary. The positivity preserving property holds for the new formulation and the overall accuracy is ensured with the use of non-uniform meshes. Numerical tests are presented in the end to show the convergence of the finite volume schemes." @default.
• W3041795894 created "2020-07-16" @default.
• W3041795894 creator A5059802527 @default.
• W3041795894 creator A5090114894 @default.
• W3041795894 date "2020-12-01" @default.
• W3041795894 modified "2023-10-18" @default.
• W3041795894 title "Positivity preserving schemes for the fractional Klein-Kramers equation with boundaries" @default.
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• W3041795894 doi "https://doi.org/10.1016/j.cnsns.2020.105444" @default.
• W3041795894 hasPublicationYear "2020" @default.
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