An Integrator for Time-Dependent Systems with Oscillatory Behavior

Many useful integrators are polynomial-based, providing high accuracy for polynomials but not necessarily for oscillatory functions. This paper describes a new integrator that provides accuracy for all these types of functions. It includes many polynomial-based formulas as a special case. Specifically, the method applies to the large class of functions which are Fourier transforms of distributions of band-limited support. Based on a Nyquist-type condition involving the highest frequency contained in the signal, both explicit and implicit methods are developed and combined in a predictor-corrector approach that provides better accuracy and allows larger stability regions.