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An analytic algorithm of Lane-Emden type equations arising in astrophysics using modified homotopy analysis method. (English) Zbl 1198.65250

Summary: Lane-Emden type equation models many phenomena in mathematical physics and astrophysics. It is a nonlinear differential equation which describes the equilibrium density distribution in self-gravitating sphere of polytropic isothermal gas, has a singularity at the origin, and is of fundamental importance in the field of stellar structure, radiative cooling, modeling of clusters of galaxies. An efficient analytic algorithm is provided for Lane-Emden type equations using modified homotopy analysis method, which is different from other analytic techniques as it itself provides us with a convenient way to adjust convergence regions even without Pade technique. Some examples are given to show its validity.

MSC:

65N99 Numerical methods for partial differential equations, boundary value problems
35Q85 PDEs in connection with astronomy and astrophysics
85A05 Galactic and stellar dynamics
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