Approximate Solution of Bratu Differential Equation Using Falker-Type Method

Abstract

In this paper, approximate solution of Bratu Differential Equation (BDEs) using Falker-type method for solving second order BDEs is presented. The approach of collocation and interpolation technique is adopted to derive the new method, which is implemented in block mode to get approximation at grids points simultaneously.  The method is of order five (5), zero-stable, consistent and convergent with good region of absolute stability. The tabular and graphical presentations of the numerical results to the problems considered, demonstrate the effectiveness of the scheme in comparison with exact equation. The method is therefore recommended for solving second order BDEs.