UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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).

Item Media

Item Citations and Data

Rights

For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.