Solving differential equations by a maximum entropy–minimum norm method with applications to Fokker–Planck equations

Publisher Website
Google Scholar
Abstract
The method of maximum entropy–minimum norm is utilized to produce a general method of solving differential equations. The technique is a generalization and extension of previous work performed by Baker-Jarvis [J. Math. Phys. 30, 302 (1989)]. It is found that introducing an additional constraint on the norm of the solution vector produces a probability distribution that is integrable over the entire real axis. A number of simplifications occur. In this extended method the Lagrange multipliers and solution vector can be solved for explicitly, thus eliminating the necessity of solving systems of nonlinear equations for the Lagrange multipliers, as was required in the previous approach. It is shown that the solution obtained is equivalent to a minimum norm approximation. The maximum entropy solution of differential equations with Fourier moments is shown to be identical to a Fourier series solution. Additionally, the new method is applied to solving the random walk and Fokker–Planck equations.

This publication has 7 references indexed in Scilit: