B-spline method for solving Bratu's problem

Abstract

In this paper, we propose a B-spline method for solving the one-dimensional Bratu's problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur.

Keywords:

• Bratu's problem
• B-spline method
• nonlinear boundary value problem
• Laplace method
• decomposition method

2000 AMS Subject Classifications :

• 34B15
• 33F05
• 65D20