Nusrat Yasmin

A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation

We construct a new general class of derivative free n-point iterative methods of optimal order of convergence 2n−1 using rational interpolant. The special cases of this class are obtained. These methods do not need Newtons iterate in the first step of their iterative schemes. Numerical computations are presented to show that the new methods are efficient and can be seen as better alternates.

A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications

Solving systems of nonlinear equations plays a major role in engineering problems. We present a new family of optimal fourth-order Jarratt-type methods for solving nonlinear equations and extend these methods to solve system of nonlinear equations. Convergence analysis is given for both cases to show that the order of the new methods is four. Cost of computations, numerical tests, and basins of attraction are presented which illustrate the new methods as better alternates to previous methods. We also give an application of the proposed methods to well-known Burgers equation.

Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices

We construct a family of derivative-free optimal iterative methods without memory to approximate a simple zero of a nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable to with-memory class. The extension of new family to the with-memory one is also presented which attains the convergence order and a very high efficiency index . Some particular schemes of the with-memory family are also described. Numerical examples and some dynamical aspects of the new schemes are given to support theoretical results.

An Optimal Eighth-Order Scheme for Multiple Zeros of Univariate Functions

We present an optimal eighth-order scheme which will work for multiple zeros with multiplicity (m>1), for the first time. Earlier, the maximum convergence order of multi-point iterative schemes was six for multiple zeros in the available literature. So, the main contribution of this study is to present a new higher-order and as well as an optimal scheme for multiple zeros for the first time. In addition, we present an extensive convergence analysis with the main theorem which confirms theoretically eighth-order convergence of the presented scheme. Moreover, we consider several real life problems which contain simple as well as multiple zeros in order to comparison with the existing robust iterative schemes. Finally, we conclude on the basis of obtained numerical results that the proposed iterative methods perform far better than the existing methods in terms of residual error, computational order of convergence and difference between the two consecutive iterations.

Stability Criteria for Volterra Integrodynamic System

We study conditions under which the solutions of linear Volterra integrodynamic system of the form are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.