A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

Abstract A numerical method is presented which allows the accurate and efficient solution of systems of linear equations of the form dz i ( x )/ dx = Σ j = 1 N 1 A ij ( x ) z j ( x ), i = 1, 2, …, N , when the solutions vary rapidly compared with the A ij ( 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.