A note on two dimensional Bratu problem

S. A. Odejide, Y. A. S. Aregbesola

In this paper, we examined the Bratu problem $$-\Delta U = ≥ambda exp[U(x,y)],\quad x,y \in D, $$ $$U(x,y) = 0,\quad x,y \in \partial D, $$ in 2-dimensions, where $ \Delta$ is the Laplace operator. The non linear equation is solved using various methods including finite difference method, weighted residual method and analytical method. Both the near exact solution and weighted residual solution, provide the upper and the lower branch solutions while the finite difference method only give the lower branch solution.