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Paper: Application of the Riccati Method to the Adiabatic Oscillations of Stars
Volume: 310, Variable Stars in the Local Group (IAU Colloquium 193)
Page: 483
Authors: Takata, M.; Loeffler, W.
Abstract: 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.
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