Numerical implementation of a perturbation theory up to the third order for rotating polytropic stars: Application to a solar model

Numerical treatment of a pertubation theory up to the third order yields quantitative estimates for an interesting polytropic solar model possessing differential rotation of Clement's type. A suitably defined reduction factor, otherwise referred to as strength, moderates the effects of the differential rotation and the so resulting limiting state represents efficiently uniform rotation of the model. The numerical results obtained are compared to respective ones derived from an original numerical implementation of a second-order perturbation theory.