On the integral solution of the one-dimensional Bratu problem

A brief survey of the properties and different treatments of the one-dimensional (1D) planar Bratu problem is presented. The treatment using Green’s function is considered. Different iterative treatments of the resulting nonlinear system of equations are discussed. Starting the solution with simple sinusoidal function having appropriate amplitude is recommended. Then the resulting system is solved using a nonlinear conjugate-gradient (NL-CG) method. The importance of the proper choice of the starting function as well as the stopping criterion of the iterative solution are stressed.