A NUMERICAL-METHOD FOR SOLVING SYSTEMS OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS WITH RAPIDLY OSCILLATING SOLUTIONS

A numerical method is presented which allows the accurate and efficient solution of systems of linear equations of the form dzi(x)/dx = Σj = 1N1 Aij(x)zj(x), i= 1, 2, ..., N, when the solutions vary rapidly compared with the Aij(x). The method consists of numerically developing a set of basis solutions characterized by new dependent variables which are slowly varying. These solutions can be accurately computed with an overhead that is substantially independent of the smallness of the scale length characterizing the solutions. Examples are given. © 1992.