A sinc-collocation method for initial value problems

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., O(M2 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.