A TAGE iterative method for the solution of non-linear singular two point boundary value problems using a sixth order discretization

We report two parameter alternating group explicit (TAGE) iteration method to solve the tri-diagonal linear system derived from a new finite difference discretization of sixth order accuracy of the two point singular boundary value problem , 0 < r < 1,  = 1 and 2 subject to boundary conditions u(0) = A, u(1) = B, where A and B are finite constants. We also discuss Newton-TAGE iteration method for the sixth order numerical solution of two point non-linear boundary value problem. The proof for the convergence of the TAGE iteration method when the coefficient matrix is real and unsymmetric is discussed. Numerical results are presented to illustrate the proposed iterative methods.