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Application of The Riccati Method to The Adiabatic Oscillations of Stars

Published online by Cambridge University Press:  12 April 2016

M. Takata  and
W. Löffler
M. Takata
Affiliation:
Department of Astronomy, School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
W. Löffler
Affiliation:
Astronomical Institute, Graduate School of Science, Tohoku University, Aramaki, Aoba, Sendai 980-8578, Japan

Abstract

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The eigenmodes of the adiabatic oscillations of stars are usually calculated numerically by solving the system of the four linear first-order differential equations using either the relaxation method or the shooting method. Finding some shortcomings in these conventional methods, we adopt another method, namely the Riccati method, in which it is not the system of the linear differential equations but the nonlinear matrix Riccati equation that is solved numerically. After describing the method, we discuss its advantages and give some demonstrations.

Type
Part 8. New theoretical developments in stellar pulsation and variability
Information
International Astronomical Union Colloquium , Volume 193: Variable Stars in the Local Group , 2004 , pp. 483 - 486
Copyright
Copyright © Astronomical Society of the Pacific 2004

References

Ascher, U.M., Mattheij, R.M.M., Russell, R.D. 1995 Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (Philadelphia: SIAM)CrossRefGoogle Scholar
Christensen-Dalsgaard, J., Mullan, D.J. 1994 MNRAS, 270, 921 Google Scholar
Gautschy, A., Glatzel, W. 1990a MNRAS, 245, 154 CrossRefGoogle Scholar
Gautschy, A., Glatzel, W. 1990b MNRAS, 245, 597 CrossRefGoogle Scholar
Glatzel, W., Gautschy, A. 1992 MNRAS, 256, 209 Google Scholar
Lopes, I.P. 2001 A&A, 373, 916 Google Scholar
Unno, W., Osaki, Y., Ando, H., Saio, H., Shibahashi, H. 1989 Nonradial Oscillations of Stars, Second Edition (Tokyo: University of Tokyo Press)Google Scholar