Abstract :
Newtonʹs method is based on a linear approximation of the function in a neighborhood of a solution point. It can be demonstrated that the error in the current iteration depends on the norm of second derivative. Instead using a higher-order approximation, the second derivative is used here to transform the function into a new one for which Newtonʹs method is faster. Compared with Newtonʹs method, the resulting method only needs to compute some corrective values for the coefficients of first derivative matrix. In computational mechanics problems, where the discretization schemes lead to very sparse matrices, a considerable improvement in the rapidity of convergence with a negligible increase in the arithmetical operations and without further memory demand, can be obtained.
