Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Nonlinear CG-like iterative methods
Journal of Computational and Applied Mathematics
Existence of positive solutions of singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Existence of multiple positive solutions of singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Large-Scale Continuation and Numerical Bifurcation for Partial Differential Equations
SIAM Journal on Numerical Analysis
An algorithm for solving boundary value problems
Journal of Computational Physics
Iterative methods for large continuation problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Comparison between Adomian's method and He's homotopy perturbation method
Computers & Mathematics with Applications
B-spline method for solving Bratu's problem
International Journal of Computer Mathematics
Hi-index | 7.29 |
A brief survey of the properties and different treatments of the one-dimensional (1D) planar Bratu problem is presented. The treatment using Green's function is considered. Different iterative treatments of the resulting nonlinear system of equations are discussed. Starting the solution with simple sinusoidal function having appropriate amplitude is recommended. Then the resulting system is solved using a nonlinear conjugate-gradient (NL-CG) method. The importance of the proper choice of the starting function as well as the stopping criterion of the iterative solution are stressed.