Applied Mathematics and Computation
Variational approach to the Lane--Emden equation
Applied Mathematics and Computation
A new analytic algorithm of Lane--Emden type equations
Applied Mathematics and Computation
A generalization of the Lane-Emden equation
International Journal of Computer Mathematics
Approximate solutions of Emden-Fowler type equations
International Journal of Computer Mathematics
Journal of Computational Physics
On the numerical solution of differential equations of Lane-Emden type
Computers & Mathematics with Applications
Further developments to the decomposition method for solving singular initial-value problems
Mathematical and Computer Modelling: An International Journal
Critical values for some non-class A geometries in thermal ignition theory
Mathematical and Computer Modelling: An International Journal
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An implicit series solution admitted by a boundary value problem modelled by a Lane-Emden equation of the second kind is obtained. The boundary value problem was derived by Frank-Kamenetskii to model the steady temperature in a vessel in which a thermal explosion is taking place. The Lane-Emden equation is reduced to an autonomous second-order ordinary differential equation by means of a coordinate transformation. The autonomous second-order ordinary differential equation is reduced to a first-order Abel equation. A power series solution of the first-order Abel equation is obtained. The power series solution of the Abel equation is transformed into an implicit series solution of the original Lane-Emden equation satisfying the boundary conditions of the original problem. We show that the implicit power series solution is valid for values of the dimensionless Frank-Kamenetskii parameter @d