An efficient method for solving Bratu equations

Modified Laplace Decomposition Method for Lane-Emden Type Differential Equations

“…Laplace Adomian decomposition method (LADM) was first proposed by Suheil A. Khuri [16], [17] and has been successfully used to find the solution of differential equations [18]- [23]. The major advantage of this method is its capability of combining the two powerful methods to obtain exact solutions for nonlinear equations.…”

Analytic approximate solution for the Bratu's problem by optimal homotopy analysis method

“…/ and also the critical value is given by see [3]. Differentiating (2) with respect to one time and setting give,…”

“…The Bratu's problem (1) nonlinear two boundary value problem with strong nonlinear term and parameter λ, this problem appears in a number of applications such as the fuel ignition model of the thermal combustion theory, the model of thermal reaction process, the Chandrasekhar model of the expansion of the Universe, questions in geometry and relativity about the Chandrasekhar model, chemical reaction theory, radiative heat transfer and nanotechnology [1,2,3]. The analytical solution of (1) in the following form:…”

Numerical experiments with the Bratu equation in one, two and three dimensions

“…Karkowski (B) M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland e-mail: januszk@th.if.uj.edu.pl the analytical solution is known. This case was also investigated numerically with help of many different methods: spline-based treatment (Abukhaled et al 2012), (modified) variational iteration method (Jin 2010;Mohyud-Din 2008), Adomian's decomposition method (Wazwaz 2005;Syam and Hamdan 2006), the Lie-group shooting method (Abbasbandy et al 2011), one-point pseudospectral collocation (Boyd 2011) and others. Our methods work fine and are in good agreement with analytical formulae and numerical results.…”