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Similarity solution of a Fokker-Planck equation with a moving, absorbing boundary Lee, Richard Tsan Ming

Abstract

A one parameter Lie group of transformations is used to derive a closed form similarity solution of the equation: [See Thesis for Equation]. A simple expression for the first passage time distribution of the general Fokker-Planck (Kolraogorov forward) equation in an irregular domain is derived, which is subsequently used to find the first passage time distributions of four equivalent problems. A new distribution is found. A small time asymptotic expansion of the integral solution of (*) is calculated in order to be pieced together to form the solution for a more general r (t). Examining the feasibility of this method, we find that it is equivalent to a simple application of Taylor expansions, and it is not better than the powerful method of transforming the irregular domain to a regular one and applying some explicit schemes. Convergence and Stability criteria are derived for an explicit method which admits an arbitrary (t).

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