The Lie-group shooting method for solving the Bratu equation

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). LGSM allows us to search a missing initial slope and moreover, the initial slope can be expressed as a function of r ∈ [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 Lie-group shooting method (LGSM) for this problem.

► The Bratu problem is transformed into a nonlinear second order boundary value problem.
► The Bratu problem is solved by the Lie-group shooting method (LGSM).
► Lie-group shooting method allows us to search a missing initial slope.