A combined approach using coupled reduced alternating group explicit (CRAGE) algorithm and sixth order off-step discretization for the solution of two point nonlinear boundary value problems

The aim of this paper is to discuss the application of two parameter coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration method to the sixth order accurate numerical solution of the two point singular boundary value problem -u″+ϕ(x,u,u′)=0, subject to natural boundary conditions. For all approximations for u and its derivatives, we use only three uniform grid points and for known variable x we use three uniform grid points and two off-step grid points. We also discuss the application of CRAGE iteration method to the singular problem. The convergence of the CRAGE iteration method is discussed in detail. We have compared the results of proposed CRAGE iteration method with the results of corresponding two parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the superiority of the proposed method.