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 2 [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.