A. Sherman et M. Mascagni, A GRADIENT RANDOM-WALK METHOD FOR 2-DIMENSIONAL REACTION-DIFFUSION EQUATIONS, SIAM journal on scientific computing, 15(6), 1994, pp. 1280-1293
An extension to two space dimensions of the gradient random walk algor
ithm for reaction-diffusion equations is presented. This family of alg
orithms is related closely to the random vortex method of computationa
l fluid dynamics. Although the computational cost is high, the method
has the desirable features of being grid free and of automatically ada
pting to the solution by concentrating elements where the gradient is
large. In addition, the method can be extended easily to more than two
space dimensions. A key feature of the method is discretization in te
rms of the dependent, rather than independent, variable, giving it fea
tures in common with Lagrangian particle methods. The method is derive
d here and its application to some simple reaction-diffusion wave prop
agation problems is illustrated.