Convergence of a random walk method for a partial differential equation

Lu, Weidong

doi:10.1090/S0025-5718-98-00917-X

Convergence of a random walk method for a partial differential equation
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Math. Comp. 67 (1998), 593-602 Request permission

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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