A sinc-collocation method for initial value problems

Abstract

A collocation procedure is developed for the initial value problem u′(t) = f(t, u(t)), u(0) = 0, using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., script O sign(M 2 exp(-κ√M)) where κ > 0 and 2M basis functions are used in the expansion. Problems on the domains ℝ = (-∞, ∞) and ℝ + = (0, ∞) are used to illustrate the implementation and accuracy of the procedure.