Rice blast, caused by Pyricularia grisea Saccardo, is an important disease in temperate flooded and tropical upland (rainfed) rice cropping systems. Planting highly or partially resistant cultivars is an effective way to control rice blast. For rice cultivars with partial resistance, using forecasts of blast epidemics to time fungicide application(s) is an important component in its control.

The dispersal of rice blast spores is an important aspect of its spatial dynamics. Diffusion models based on gradient transfer theory have been used to study spore dispersal, and they usually require numerical methods for solutions because of the complexity. Different numerical methods have been developed and tested for their accuracy in atmospheric diffusion studies. Because our interest in studying pest epidemics is confined to a much smaller space (several orders of magnitude smaller), methods suitable for atmospheric diffusion studies need to be tested and/or modified in the context of spore and insect dispersal.

The emphasis of our research is to compare the accuracy of numerical methods in solving a simplified three-dimensional advection-diffusion equation as applied to the study of spore and insect dispersal. Our basic assumption was that if a numerical method works well in a simplified situation where analytical solutions could be obtained, it should also work well in similar but more complicated situations where analytical solutions could not be obtained. We hope the results from the study could help us select and use appropriate numerical methods in studying the spatial dynamics of spores and insects.

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