A GRADIENT RANDOM-WALK METHOD FOR 2-DIMENSIONAL REACTION-DIFFUSION EQUATIONS

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.