Local Solutions of Laplace, Heat, and Other Equations by Itô Processes
Publication: Journal of Engineering Mechanics
Volume 123, Issue 8
Abstract
A method is presented for finding the solution of deterministic partial differential equations at an arbitrary point of the domain of definition of these equations referred to as the local solution. The method is based on the Itô calculus, properties of diffusion processes, and Monte Carlo simulation. The theoretical background of the proposed method is relatively difficult. However, the method has attractive features for applications. For example, the numerical algorithms based on the proposed method are simple, stable, accurate, local, and ideal for parallel computation. Numerical examples from mechanics are presented to demonstrate the use and the accuracy of the proposed method.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Aug 1, 1997
Published in print: Aug 1997
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