I work in the numerical solution of partial differential equations, especially those modeling combusion, solid mechanics, wave propagation, and fluid dynamics. Development of adaptive numerical procedures for both finite differences and spectral methods. Computation and analysis of pattens in combustion, including both gaseous combustion nd solid fuel combustion, a procedure for the synthesis of materials usig highly exothermic reactions. Analysis and computations of integro-partial dfferential equations modeling nonloal interactions. An example of such a system involves competing populations where the computation or a scarce resource, e.g., water, food or air, depends on not just the population at a specific point but on a weighted average of the populations in a neighborhood of the point.