An $O(h^4)$ accurate cubic spline TAGE method for nonlinear singular two point boundary value problems

Abstract

In this paper, we propose two parameter alternating group explicit (TAGE) method for the numerical solution of Image, $u'' + \frac {\alpha}{r}\ u'$ – $\frac{\alpha} {r^2}\ u = f(r), 0 < r < 1$ using a fourth order accurate cubic spline method with specified boundary conditions at the end points. The proof of convergence of the TAGE method when the coefficient matrix is unsymmetric and real is presented. We also discuss Newton-TAGE method for the numerical solution of nonlinear singular two point boundary value problem using the cubic spline method with same accuracy of order four. Numerical results are provided to illustrate the viability of the proposed TAGE method