Introduction

A historical sketch of the nonlinear theory of variable stars is outlined briefly. The main break-through came from the hydrodynamic study of stellar pulsation. From a theoretical point of view, coupling needs to be discussed more carefully. The impact of new opacities on the astrophysical problems is also discussed.     

Introduction

Seven algorithms are investigated for integrating stellar orbits in axisymmetric and time-independent galactic models. We find that for this purpose, impressive gains over older methods are possible with higher order Runge-Kutta methods and variable order methods.