Research Article
A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order and Its Dynamics
Figure 1
Geometric modification of Newton-Secant method. is the point given by Newton’s method. In the next step, using condition (4), we have that . Thus the line passing through the points and gave us the better approximation to the root . This approximation is better than given by Newton’s method. The concave case is analogous to convex case.
(a) Convex case |
(b) Concave case |