Faculty and Researchers
A New Derivative-Free Method to Solve Nonlinear Equations
(MDPI, 2021)
A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated. It is also shown that the method ...
A New Trigonometrically-Fitted Method for Second Order Initial Value Problems
(Monterey, California. Naval Postgraduate School, 2020-12); NPS-MA-20-001
Numerical schemes approximating the solution of ordinary initial value problems interpolate polynomial up to a certain degree. Brock and Murray have suggested in 1952 to interpolate exponential functions when the solution ...
High-order nonreflecting boundary conditions for the dispersive shallow water equations
(Elsevier, 2003)
Time-dependent dispersive shallow water waves in an unbounded domain are considered. The infinite domain is truncated via an artificial boundary , and a high-order non-reflecting boundary condition (NRBC) is imposed on . ...
A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points
(MDPI, 2019-06)
A generic family of optimal sixteenth-order multiple-root finders are theoretically developed from general settings of weight functions under the known multiplicity. Special cases of rational weight functions are considered ...
Developing high order methods for the solution of systems of nonlinear equations
(Elsevier Ltd., 2019)
Two families of order six for the solution of systems of nonlinear equations are developed and compared to existing schemes of order up to six. We have found that one of the methods in the literature has been rediscovered. ...
Numerical Solution of a Nonlinear Diffusion Model with Memory
(Monterey, California. Naval Postgraduate School, 2018-11); NPS-MA-18-001
Finite difference approximation of a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Here we discuss the model described by a nonlinear integro-differential ...
Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics
(MDPI, 2018-12-21)
Developed here are sixteenth-order simple-root-finding optimal methods with generic
weight functions. Their numerical and dynamical aspects are investigated with the establishment of a
main theorem describing the desired ...
Dynamics of some one-point third-order methods for the solution of nonlinear equations
(ISPACS, 2018)
In this paper we have considered 32 one-point methods of cubic order to obtain simple zeros of a nonlinear function. These schemes are constructed by decomposition of previously known schemes. We have used the idea of ...
Comparative study of methods of various orders for finding repeated roots of nonlinear equations
(Elsevier B.V., 2017-10-11)
In this paper we are considering 20 (families of) methods for finding repeated roots of a nonlinear equation.The methods are of order up to 8. We use the idea of basin of attraction to compare the methods. We found that ...
Comparative study of methods of various orders for finding repeated roots of nonlinear equations
(Elsevier Editorial System for Journal of Computational and Applied Mathematics, 2017)
In this paper we are considering 20 (families of) methods for
finding repeated roots of a nonlinear equation. The methods are of order
up to 8. We use the idea of basin of attraction to compare the methods.
We found ...