A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

Figure 3

Schematic diagram of the new iterative algorithm associated with the numerical continuation procedure (see Section 3). Notations: (i) the dashed straight arrow denotes the true tangent straight line (); (ii) the bold solid straight arrow is the modified tangent straight line for the converged point (square point) at the time (); (iii) the perpendicular solid straight line with the bold solid straight arrow is the iterative line at the time (); (iv) the other parallel solid straight lines with respect to the bold solid straight arrow are the th iterative iterative lines at the time ( with   ) with the th iterative points (circle points) such that (iv-a) if , then ; (iv-b) if , then ; and (iv-c) if , then .

(a)

(b)