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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 $r \in [0,1]$, 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.

65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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