A class of new, non-symmetric solutions are computed for the Bratu problem governed by the partial differential equation \(\Delta\theta= \varepsilon e^{\theta/(1+\mu\theta)}\) in a two-dimensional rectangular domain. Also a perturbed Bratu problem is examined with convection as an additional heat transport mechanism and Rayleigh number \(Ra\) and tilt angle \(\varphi\) as additional parameters.
Solution curves in the five-dimensional parameter space are calculated by Euler-Newton continuation starting from small values of \(\varepsilon\) and \(Ra\). Limit points are located by using an extended system. The calculations are carried out at different grid sizes to establish the presence of the asymmetric solutions independently of the grid size; by extrapolating the mesh size down to zero it is shown that the asymmetric branches remain distinct. The stability of the computed solutions with respect to divergence is calculated by a power iteration method.