An accurate h-pseudospectral method for numerical solution of the Bratu-type equations

In this study, an accurate method is developed for solving both initial and boundary value problems of the Bratu-type equations arising in various physical and chemical phenomena. In particular, we investigate the Bratu-Gelfand problem, which is of interest to many researchers because of the behavior of the solution. In the designed methodology, the problem is discretized using a h-pseudospectral method and therefore, solving the problem is reduced to solve a system of nonlinear equations. Numerical results of two examples are presented at the end and the comparison is made with the existing numerical or analytical solvers to show the efficiency and accuracy of the proposed method.

Keywords:

Bratu equations , Initial and boundary value problems , H-pseudospectral method , Legendre-Gauss-Radau points