Abstract:
In this paper, a bivariate spectral quasilinearization
method is used to solve the highly nonlinear
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
methodwere compared with results from nite di erences
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.
