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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).
Item Metadata
Title |
Similarity solution of a Fokker-Planck equation with a moving, absorbing boundary
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1980
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Description |
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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Type | |
Language |
eng
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Date Available |
2010-03-19
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Provider |
Vancouver : University of British Columbia Library
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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.
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DOI |
10.14288/1.0079352
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Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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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.