Novel fast and accurate methods for partial differential equations

University Of Delaware, Newark DE

Investigators

Abstract

The investigator will research high-order and pseudospectral methods for the numerical approximation of solutions of linear and nonlinear partial differential equations of evolution. The proposed activities divide into methods for time and space: high-order time stepping without severe stability restrictions, even in the presence of stiffness, and the use of radial basis functions for spatial differencing (with emphasis on the need for efficient and stable computation). Analytical and numerical techniques will be used to frame and solve interesting issues. Computational simulation is a vital part of research and design in science and engineering. Many problems of academic and industrial interest remain beyond present computing power, and there are also significant benefits in solving tractable problems more quickly and accurately. Innovations in both hardware and software will be needed to continue the progress of recent decades. The research in this proposal is directed at finding and improving the techniques that will be used in scientifically oriented software in the near future. There is an emphasis on phenomena that propagate or evolve over long distances or times. Specific fields of study that could benefit include optical communications, imaging by electromagnetic or acoustic illumination, and computational chemistry.