On the Numerical Solution of Stiff Linear Systems of the Oscillatory Type

Abstract

A method is presented for the numerical solution of a stiff linear system of O.D.E.,The stiffness is assumed to arise from large imaginary parts of some of the eigenvalues of P(t). The large imaginary parts cause a rapidly oscillating component to be superimposed on X(t) forcing the use of very small integration steps. This difficulty is overcome by "filtering out" the large eigenvalues making it possible to calculate the smooth component of X with a reasonable stepsize. An explicit formula is als0 given for the oscillatory component of X. Finally, results of numerical experiments are presented.A second article by the same authors is to appear which includes another method of solution for similar kinds of problems.

Heterogeneous multiscale methods for stiff ordinary differential equations

“…Computationally, averaging approaches appeared in many places, e.g., in [27,34] and [25,26], and recently in [9] and [22].…”