Mathematical Sciences: Workshop on the Method of Lines for Time-Dependent Problems

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The investigator and his colleagues organize a workshop on the method of lines for solving partial differential equations. Major themes are ordinary differential equation theory and software as applied in method of lines (MOL) algorithms for time-dependent partial differential equations, theoretical aspectsof MOL algorithms including error estimation and stability considerations, the design and development of MOL software, scientific and engineering applications of MOL software, and the impact of modern computer architectures, particularly distributed memory parallel processors, on the structuring and implementation of MOL algorithms. The workshop brings together both new and experienced researchers in the numerical analysis of ordinary and partial differential equations to discuss the interaction of their MOL research. In particular, it facilitates collaboration among theoreticians, designers of MOL software packages, and researchers applying the MOL to large scale problems, with the aim of improving parallel implementations, and identifying theoretical and practical constraints impacting MOL algorithms. Many issues of considerable current interest, such as global climate change or the behavior of contaminants in the atmosphereor in groundwater, are influenced by a variety of physical and chemical processes. These processes can be simulated by mathematical models solved by techniques in this workshop. As tools in the study of these models, researchers participating in the workshop are developing advanced computational techniques for use on high performance computing systems involving parallel processing. On a computer of this type, several tasks, sometimes as many as several hundred, can be executed simultaneously. As a consequence, it becomes feasible to solve more realistic, and usually more complex, models than those previously considered. The computational speed afforded by techniques discussed in this workshop permits comprehensive models that can lay a firmer scientific foundation for policy decisions. With such models, the short-and long-term effects of a change in policy, for example in emission standards, can be effectively predicted before a proposed change is actually implemented.