A variational method for solving two-dimensional Bratu's problem

Abstract

In this paper we propose a variational method in order to solve Bratu Problem for two dimension in an adequate space of biquadratic spline functions. The solution is obtained by resolving a sequence of boundary value problems. We study some characterizations of the functions of such sequence and we express them as some linear combination of biquadratic spline bases functions. We nish by showing some numerical and graphical examples in order to prove the validity and the e ectiveness of our method.