On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem

Abstract

In this paper, a bivariate spectral quasi-linearization method is used to solve the highly non-linear two dimensional Bratu problem. The two dimensional Bratu problem is also solved using the Chebyshev spectral collocation method which uses Kronecker tensor products. The bivariate spectral quasi-linearization method and Chebyshev spectral collocation method solutions converge to the lower branch solution. The results obtained using the bivariate spectral quasi-linearization method were compared with results from finite differences method, the weighted residual method and the homotopy analysis method in literature. Tables and graphs generated to present the results obtained show a close agreement with known results from literature.

Keywords

• bratu problem
• quasi-linearization
• chebyshev-gauss-lobatto points
• bivariate interpolation
• spectral collocation
• 02.30.hq
• 02.60.cb
• 02..60.lj
• 02.70.hm