A class of rapidly convergent interative Methods for Problems in mathematical Modelling

Methods with the convergence order p 2 (Newton`s, tangent hyperbolas, tangent parabolas etc.) and their approximate variants are studied. Conditions are presented under which the approximate variants preserve their convergence rate intrinsic to these methods and some computational aspects (possibilities to organize parallel computation, globalization of a method, the solution of the linear equations versus the matrix inversion at every iteration etc.) are discussed. Polyalgorithmic computational schemes (hybrid methods) combining the best features of various methods are developed and possibilities of their application to numerical solution of two-point boundary-value problem in ordinary differential equations and decomposition-coordination problem in convex programming are analyzed.