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Convergence of a random walk method for a partial differential equation

Author: Weidong Lu
Journal: Math. Comp. 67 (1998), 593-602
MSC (1991): Primary 65C05, 65M99
MathSciNet review: 1443122
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Abstract: A Cauchy problem for a one–dimensional diffusion–reaction equation is solved on a grid by a random walk method, in which the diffusion part is solved by random walk of particles, and the (nonlinear) reaction part is solved via Euler’s polygonal arc method. Unlike in the literature, we do not assume monotonicity for the initial condition. It is proved that the algorithm converges and the rate of convergence is of order $O(h)$, where $h$ is the spatial mesh length.

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Additional Information

Weidong Lu
Affiliation: Department of Mathematics, Fudan University, Shanghai, 200433, China

Keywords: Random walk method, partial differential equation, Cauchy problem.
Received by editor(s): July 20, 1995
Received by editor(s) in revised form: December 11, 1996
Additional Notes: This work is partially supported by the Chinese State Education Commission Natural Science Foundation.
Article copyright: © Copyright 1998 American Mathematical Society