In this paper, a spectral quasi-linearization method (SQLM) is used to solve the non-linear Bratu problem in its one dimensional planar coordinate form. The numerical results obtained are verified by comparison with the exact solution and some results in literature. The results obtained indicate that SQLM gives more accurate solutions than the B-spline method and the iterative finite difference method. Increasing the number of collocation points in the SQLM improves the results but code requires more run time. We conclude that the SQLM is highly accurate, easy to implement and computationally efficient.

Bratu problem, quasi-linearization, spectral collocation, Gauss-Lobatto grid points, Chebyshev differentiation.