A cubic spline collocation method for solving Bratu’s Problem

Abstract

This paper, we develop a numerical method for solving a Bratu-type equations by using the cubic splinecollocation method (CSCM) and the generalized Newton method. This method converges quadratically if arelation-ship between the physical parameter ? and the discretization parameter h is satisfied. An error estimatebetween the exact solution and the discret solution is provided. To validate the theoretical results, Numericalresults are presented and compared with other collocation methods given in the literature.Keywords: Bratu-type equations, Boundary value problems, Cubic spline collocation method.