THE ORDER AND SPEED OF CONVERGENCE FOR THE k-FOLD PSEUDO-OLVER'S METHOD LOCATING A SIMPLE REAL ZERO

A convergence behavior is under investigation near a simple real zero for the k-fold pseudo-Olver's method defined by extending the classical Olver's method. The order of convergence is shown to be at least k+3. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. Various numerical examples with a proposed zero-finding algorithm are successfully confirmed with the use of symbolic and computational ability of Mathematica.