arXiv subjects

Malik Zaka Ullah

Publications and source records attributed to Malik Zaka Ullah.

4 recordsLinked to original sources

arXiv2020

Impact of higher-order effects on dissipative soliton in metamaterials

We study the influence of higher-order effects such as third order dispersion (TOD), fourth order dispersion (FOD), quintic nonlinearity (QN), self steepening (SS) and second order nonlinear dispersion (SOND) on the dynamics of dissipative soliton (DS) in metamaterials. Considering each higher-order effect as a perturbation to the system and following Lagrangian variational method, we demonstrate stable dynamics of DS as a result of the interplay between different higher-order effects. We also perform numerical analysis to confirm the analytical results.

nlin.PS↗

arXiv2013

A correction note on "Three-step iterative methods for nonlinear equations" and generalization of method

In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated a theorem (\textbf{Theorem 2.3}) to prove the cubic order of convergence but the given proof does not show cubic order of convergence. Actually, the mathematical derivation steps to develop the \textbf{Algorithm 2.3} are wrong. In this note, we present the correct mathematical developments and finally provide computational order of convergence in the favor of our claim and provide the generalization of the method.

math.NA↗

arXiv2013

A correction note on "New iterative schemes for nonlinear equations"

In Noor (2007)[Muhammad Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput. 187 (2007) 937-943], proposed an algorithm namely \textbf{Algorithm 2.4} and established a proof to show cubic convergence. The presented proof is wrong. In this article, we show that \textbf{Algorithm 2.4} is not cubically convergent.

math.NA↗

arXiv2013

Eighth-order Derivative-Free Family of Iterative Methods for Nonlinear Equations

In this note, we present an eighth-order derivative-free family of iterative methods for nonlinear equations. The proposed family shows optimal eight-order of convergence in the sense of the Kung and Traub conjecture \cite{5} and is based on the Steffensen derivative approximation used in the Newton-method. As a final step, having in mind computational purposes, a derivative-free polynomial base interpolation is used in order to get optimal order of convergence with only four functional evaluations. Numerical esperiments and few issues are discussed at the end of this note.

math.NA↗