Abstract
Explicit and implicit difference schemes discretely conserving mass and non-negativity (discrete diffusion models) are developed for linear Fokker-Planck equations in one space dimension under conditions of periodicity or reflecting boundaries and under interface conditions. Possible generalizations to inhomogeneous equations, to inhomogeneous boundary conditions, and to nonlinear problems are hinted at, and applications to numerical treatment of indeterminate two-point boundary value problems are pointed out.
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Gorenflo, R. (1978). Conservative Difference Schemes for Diffusion Problems. In: Albrecht, J., Collatz, L., Hämmerlin, G. (eds) Numerische Behandlung von Differentialgleichungen mit besonderer Berücksichtigung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 39. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5566-2_7
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DOI: https://doi.org/10.1007/978-3-0348-5566-2_7
Publisher Name: Birkhäuser, Basel
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