A Fourier Approach to the Analysis and Design of Numerical Methods for Differencial Equations

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The numerical solution of ordinary and partial differential equations (ODEs and PDEs) provides an important class of large scale scientific computing problems. Fourier analysis has been used by applied mathematicians as a simple and effective tool to analyze the numerical properties of approximation schemes and solution methods for ODEs and PDEs. This includes three main objectives: (1) exploiting Fourier tools used in the areas of digital filtering and digital control for solving ODEs and elliptic PDEs, (2) analyzing numerical ODE and elliptic PDE algorithms with Fourier techniques so that they can be understood by electrical engineers in a more familiar setting, and (3) development of new parallel algorithms and study of their performnce on parallel algorithms and study of their performance on parallel computers such as the Connection Machine CM/2 and Alliant FX/80.