Abstract
Numerical solution differential equation of Lane-Emden type is considered by Padé approximation. We apply these method to two examples. First differential equation of Lane-Emden type has been converted to power series by one-dimensional differential transformation, then the numerical solution of equation was put into Padé series form. Thus, we have obtained numerical solution differential equation of Lane-Emden type.
Highlights
Lane-Emden equations have the following form 1–4 :y k x y f x, y g x, 0 ≤ x ≤ 1, k ≥ 0, 1.1 y 0 A, y 0 B, where A and B are constants, f x, y is a continuous real-valued function, and g x ∈ C 0, 1
Lane-Emden equations are singular initial value problems relating to second-order ordinary differential equations ODEs which have been used to model several phenomena in mathematical physics and astrophysics such as thermal explosions 5, the thermal behavior of a spherical cloud of gas, isothermal gas spheres, and thermionic currents 5
The variational iteration method is used to solve differential equations arising in astrophysics including the LaneEmden equation 7, 8
Summary
Lane-Emden equations have the following form 1–4 :. Lane-Emden equations are singular initial value problems relating to second-order ordinary differential equations ODEs which have been used to model several phenomena in mathematical physics and astrophysics such as thermal explosions 5 , the thermal behavior of a spherical cloud of gas, isothermal gas spheres, and thermionic currents 5. Wazwaz 6 has given a general way to construct exact and series solutions to Lane-Emden equations by employing the Adomian decomposition method. A numerical solution of Lane-Emden equations is given based on the Legendre wavelets methods 4. Differential equation of Lane-Emden type has been converted to power series by one-dimensional differential transformation; differential transformation was introduced first by Zhou 12. We obtain numerical solution differential equation of Lane-Emden type
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