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Solution of Mathieuís equation by Runge-Kutta integration

By T. Funada1, J. Wang2, D.D. Joseph2, N.Tashiro1 and Y.Sonoda1

1Department of Digital Engineering, Numazu College of Technology, 3600 Ooka, Numazu, Shizuoka, 410-8501, Japan
2Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA

(April, 2005)

Abstract

In this note we shall show that Mathieuís equation for x(t)

may be efficiently and accurately integrated by the Runge-Kutta (RK) method under the initial conditions

for the even Mathieu functions cen(t, q) → cos (nt) as q → 0 and

for the odd Mathieu functions sen(t, q) → sin (nt) as q 0.