This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences of the National Science Foundation. This program supports the purchase of special purpose computing equipment dedicated to the conduct of research in the mathematical sciences. This equipment is required for several research projects and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers and with substantial cost-sharing from the institutions submitting the proposal. This program is an example of academic, corporate, and government cooperation in the support of the basic research in the mathematical sciences. This equipment will be used to support four research projects in the Department of Engineering Science and Applied Mathematics of Northwestern University. The names of the investigators and the titles of their projects follow: Numerical Study of Non-adiabatic Gaseous Fuel Combustion, Bayliss and Matkowsky; Numerical Study of Gasless Combustion, Bayliss and Matkowsky; Numerical Solution of Integro-partial Differential Equations in Stochastic Dynamics, Matkowsky; and Numerical Simulations of Activation in Stochastic Dynamics, Matkowsky.