Compact alternating group explicit method for the cubic spline solution of two point boundary value problems with significant nonlinear first derivative terms

In this paper, we report the application of two parameter coupled alternating group explicit (CAGE) iteration and Newton-CAGE iteration methods for the cubic spline solution of non-linear differential equation u = f(r,u,u ) subject to given natural boundary conditions. The error analysis for CAGE iteration method is discussed in details. We compared the results of proposed CAGE iteration method with the results of corresponding two parameter alternating group explicit (TAGE) iteration method to demonstrate computationally the efficiency of the proposed method.