New applications for a combined differential transformation method with Adomian ploynormals in Astrophysics

摘要

Very recently, the difficulty in solving nonlinear differential equations by the differential transformation method has been solved for complex nonlinear terms. This goal has been achieved via a general formula for computing the differential transform components of any analytic nonlinear function. The reliability and the efficiency of the improved method is demonstrated in the present paper, where several nonlinear initial and boundary value problems, including Troesch's problem, the white-dwarf equation, isothermal gas spheres and the Lane-Emden equation are solved. As a matter of fact, the newly developed method offers a computationally easier approach to solve nonlinear ordinary differential equations for any analytic nonlinearity if compared with the standard method, which of course increases its applicability.