Application of Block Method for Solving Nonlinear Two Point Boundary Value Problem

The nonlinear two point boundary value problem (TPBVP) exists in a wide variety of applications in engineering and sciences including modeling of chemical reactions and heat transfer. In this paper, we propose a two point direct block method via multiple shooting technique to solve Bratu's and Troesch's problem. The two point direct block method will solved these problems directly without reducing it to first order ODEs and estimate the solutions at two points simultaneously. Lagrange interpolation polynomial was implemented in the derivation of the proposed block method. The block method will estimate the solutions using constant step size via multiple shooting technique. Multiple shooting is a combination of several simple shooting techniques and it will employ the three-step iterative method for checking the convergent of the guessing value for the next iteration. Numerical experiments demonstrate the computational efficiency of the two point direct block method.