This project investigates SINC methods for ODES. The following tasks are undertaken; (1) develop a SINC ODE-IVP (sequential and/or parallel) program package for solving ordinary differential equation initial value problems, (2) develop a (sequential and/or parallel) program package to evaluate multidimensional convolution integrals, (3) write a program package which uses the Maple program to reduce a differential or integral equation to a system of algebraic equations, based on SINC derivative and/or SINC convolution collocation, (4) write program packages, based on SINC derivative and/or SINC convolution collocation, to solve problems which are important for ongoing research at the University of Utah (the forward problem Maxwell equations, with variable permeability and permittivity, but with conductivity; the solution, based on SINC convolution collocation, of the integral equation formulation of a scalar conservation law problem in two and three dimensions), and (5) comparison studies of complexity and stability of SINC and classical methods, especially in areas in which one can expect SINC methods to have advantages over methods, such as for problems with singularities, problems over unbounded regions, boundary layer problems, stiff problems, and intensive problems such as the solution of the above cited equations.
