Maximum-entropy approach with higher moments for solving Fokker–Planck equation

The maximum-entropy method with higher number of moments is used to solve the Fokker–Planck equation. An adopted Newton method is used to iterate the maximum entropy set of equations. The method is used to calculate the probability density function of the Fokker–Planck equation. The calculations are carried out for three examples. (1) The bistable systems of double well potential that is used in many problems related to the fluctuation and relaxation processes in far from equilibrium systems. (2) The Malthus–Verhulst model, which is used to study the evolution of the number of individuals of an ecological species and the evolution of the intensity of the laser light. (3) The Black–Scholes equation used in financial market option pricing. Although the maximum-entropy approach has several advantages, it is not convergent at large times and so cannot be used to calculate the steady state solution.