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A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables, which ensures the global stability of discretization. Convection-diffusion equations are notorious for their lack of stability, arising from the algebraic interaction of the convection and diffusion terms. Unexpectedly, our implemented numerical algorithm proves to be faster than computing exact solutions derived for a special case, while remaining reasonably accurate, as demonstrated in our runtime and error analysis.MSC class: 65M08 (primary); 65M12, 35C05 (secondary).

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A novel system providing effective and efficient access t o video archives for mobile users communicating over low bandwidth error-prone wireless links is proposed. T h e developed system has three components: First, the middleware, implemented as mobile proxy server located a t the mobile support station, is chosen for the seamless integration of both mobile users and video servers by hiding the specific details of the underlying system. Second, for efficient video transmission, our three-dimensional significant-linked connected component analysis video codec well suited for wireless environments, is used. Finally, multilayer transmission error control mechanism is applied to cope with channel errors. As a result, no additional requirements are imposed on the mobile client and video server so that mobile users interact with the server i n exactly the same way as stationary users, and all they experience are better picture qualit,y, less jerky video, and shorter delays.

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