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The Fokker-Planck equation: methods of solution and applications H. Risken
Publisher: Springer-Verlag

The equations are more interesting for \beta > 0 . We shall also solve the heat equation with different conditions imposed. Since r = 0 is a solution, the origin is still an equilibrium. We shall solve the classic PDE's. This has two solutions, r = 0 and r = \sqrt{\beta} . Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives. Other important applications re-. The Laplace Transform Solutions of PDE. Solutions of the fractional Fokker-Planck equation and to study statistical properties of the tempered subdiffu- sion via Monte Carlo methods. Diffusion equations on Cantor sets. Jumarie, “Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions,” Chaos, Solitons and Fractals, vol. In can be very annoying in the literature if someone uses a Fourier transform with out stating which one. The Fokker-Planck Equation: Methods of Solution and Applications. The heat, wave and Laplace equations by Fourier transforms. The example we will present later is a Fokker-Plank equation. But now it's not stable: if r is between 0 .. The general method of solution will be the same. A formal analogy of the Fokker–Planck equation with the Schrodinger equation allows the use of advanced operator techniques known from quantum mechanics for its solution in a number of cases. Risken: The Fokker-Planck Equation: Methods of Solution and Applications (Springer, Berlin, 1989) 2nd ed.