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The Fokker-Planck equation: methods of solution

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

The Fokker-Planck equation: methods of solution and applications


The.Fokker.Planck.equation.methods.of.solution.and.applications.pdf
ISBN: 0387130985,9780387130989 | 485 pages | 13 Mb


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




Risken, The Fokker-Planck Equation: Methods of Solutions and Applications, Springer Series in Synergetics, 2nd ed. The main topics are the Witten model, supersymmetric classical mechanics, shape-invariant potentials and exact solutions, supersymmetry in classical stocastic dynamics and supersymmetry in the Pauli & Dirac equations. Solutions of the fractional Fokker-Planck equation and to study statistical properties of the tempered subdiffu- sion via Monte Carlo methods. Encompassing both theory and practice, this original text provides a unified approach to the analysis and generation of continuous, impulsive and mixed random processes based on the Fokker-Planck equation for Markov processes. The treatment of Fokker–Planck equations with changes of variable is reviewed, followed by the transformation of diffusion equations into Schrödinger-like form, the application of supersymmetric quantum mechanics We investigate solutions of the Fokker–Planck diffusion equation with spatiotemporally varying drift and diffusion coefficients, .. A suitable version of the Fokker-Planck FP equation. Cooper, Klein and Sukhatme (1995) give a good general introduction to supersymmetry methods in quantum mechanics. The Fredholm-type equations, which have many applications in mathematical physics, are then considered. We consider the local Lyapunov exponents LLEs, in particular, the case The closed-form stationary solutions to the FP equation are in excellent accord with numerical simulations for both the unmagnetized and magnetized .. Other important applications re-. Topics include: supersymmetry in the Fokker-Planck & Lengevin equations and the implications of good/broken supersymmetry. Chapter 8 discusses A table of applications of supersymmetry in theoretical physics is also included. The properties of hybrid There has recently been much attention devoted to the search for better and more efficient solution methods for determining a solution, approximate or exact, analytical or numerical, to nonlinear models [3–5]. The method is based upon hybrid function approximate.