Showing papers by "Guo-Wei Wei published in 1997"

Lagrange Distributed Approximating Functionals

Abstract: Lagrange distributed approximating functionals (LDAFs) are proposed as the basis for a new, collocation-type method for accurately approximating functions and their derivatives both on and off discrete grids. Example applications are presented to illustrate the use of LDAFs for solving the Schr{umlt o}dinger equation and Fokker-Planck equation. LDAFs are constructed by combining the DAF concept with the Lagrange interpolation scheme. {copyright} {ital 1997} {ital The American Physical Society}

Distributed approximating functional approach to the Fokker–Planck equation: Time propagation

Abstract: The Fokker–Planck equation is solved by the method of distributed approximating functionals via forward time propagation. Numerical schemes involving higher-order terms in Δt are discussed for the time discretization. Three typical examples (a Wiener process, an Ornstein–Uhlenbeck process, and a bistable diffusion model) are used to test the accuracy and reliability of the present approach, which provides solutions that are accurate up to ten significant figures while using a small number of grid points and a reasonably large time increment. Two sets of solutions for the bistable system, one computed using the eigenfunction expansion of a preceding paper and the other using the present time-dependent treatment, agree to no fewer than five significant figures. It is found that the distributed approximating functional method, while simple in its implementation, yields the most accurate numerical solutions yet available for the Fokker–Planck equation.

Distributed approximating functional approach to the Fokker-Planck equation: Eigenfunction expansion

Abstract: The distributed approximating functional method is applied to the solution of the Fokker–Planck equations. The present approach is limited to the standard eigenfunction expansion method. Three typical examples, a Lorentz Fokker–Planck equation, a bistable diffusion model and a Henon–Heiles two-dimensional anharmonic resonating system, are considered in the present numerical testing. All results are in excellent agreement with those of established methods in the field. It is found that the distributed approximating functional method yields the accuracy of a spectral method but with a local method’s simplicity and flexibility for the eigenvalue problems arising from the Fokker–Planck equations.