Families of two-step fourth order P-stable methods for second order differential equations

Families of two-step fourth order P-stable methods for second order differential equations

This paper deals with a class of symmetric (hybrid) two-step fourth order P-stable methods for the numerical solution of special second order initial value problems. Such methods were proposed independently by Cash [1] and Chawla [3] and normally require three function evaluations per step. The purpose of this paper is to point out that there are some values of the (free) parameters available i...

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations

Some new higher algebraic order symmetric various-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Basing on this formula, calculation of free parameters is performed to minimize the phase-lag. An explicit symmetric multistep method is presented. This method is of higher algebraic order and is fitted both exponentially and trigonomet...