COMPARATIVE PROPERTIES OF SOME TIME DIFFERENCING SCHEMES FOR LINEAR AND NONLINEAR OSCILLATIONS

Abstract

The properties of 13 computational methods for the integration of first-order differential equations in time are studied. Special attention is given to the representation of periodic fluctuations in a simple spectral baroclinic model of the atmosphere. Errors in the energy, three dimensional scale, and frequency for linear and nonlinear oscillations are evaluated. Comparisons of both one-step and two-step methods are made. It is found that the two-step schemes compare favorably with one-step methods only when given the advantage of a smaller time increment. Even then, it is concluded that certain one-step procedures incorporating two or more extrapolations over each constant increment of time produce errors which grow most slowly. With small time increments, these errors are generally made smallest by increasing the number of time extrapolations at each step rather than by decreasing the time increment.