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The Lie-group shooting method for solving the Bratu equation. (English) Zbl 1222.65067
Summary: For the Bratu problem, we transform it into a non-linear second order boundary value problem, and then solve it by the Lie-group shooting method (LGSM). The LGSM allows us to search a missing initial slope and moreover, the initial slope can be expressed as a function of $r\in \left[0,1\right]$, where the best $r$ is determined by matching the right-end boundary condition. The calculated results as compared with those calculated by other methods, illuminate the efficiency and precision of the LGSM for this problem.
##### MSC:
 65L10 Boundary value problems for ODE (numerical methods) 34B15 Nonlinear boundary value problems for ODE