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math.NA2026
Diagonal Frog meets ADI: trading matrix exponentials for rational maps in the Fokker--Planck equation
Andrey Itkin, Rakhymzhan Kazbek
A companion paper \cite{ItkinDF2026} introduced the Diagonal Frog (DF) positivity-preserving schemes for anisotropic Fokker--Planck equations, advancing each directional substep by…
math.NA2026
Flux-Corrected Diagonal Frog: second order and positivity at all time steps
Andrey Itkin
By Godunov's theorem, linear second-order finite-difference schemes for the Fokker-Planck equation cannot preserve positivity. The Diagonal Frog (DF) framework previously bypassed…
math.NA2026
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
Andrey Itkin
The Fokker-Planck equation is fundamental to statistical mechanics, yet in settings with multiple state variables, anisotropic (cross-) diffusion, and jumps, conventional discretiz…