Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation
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DOI: 10.1016/j.ijleo.2020.164335
Abstract: Abstract The generalized nonlinear eighth-order Schrodinger equation with third, fifth, seventh and ninth power of nonlinearity is studied. This equation can be used for description of the pulse propagation in optical fiber. It is demonstrated… read more here.
Keywords: eighth order; highly dispersive; dispersive optical; nonlinear eighth ... See more keywords
Optimal fourth- and eighth-order of convergence derivative-free modifications of King’s method
Sign Up to like & getrecommendations! Published in 2019 at "Journal of King Saud University - Science"
DOI: 10.1016/j.jksus.2018.12.001
Abstract: Abstract Starting by King’s method, we propose a modified families of fourth- and eighth-order of convergence iterative methods for nonlinear equations. The fourth-order method requires at each iteration three function evaluations, while the eighth-order methods… read more here.
Keywords: order convergence; order; eighth order; king method ... See more keywords
Breathers and rogue waves for an eighth-order variable-coefficient nonlinear Schrödinger equation in an ocean or optical fiber
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DOI: 10.1080/17455030.2016.1275879
Abstract: An eighth-order variable-coefficient nonlinear Schrödinger equation in an ocean or optical fiber is investigated in this paper. Through the Darboux transformation (DT) and the generalized DT, we obtain the breather and rogue wave solutions. Choosing… read more here.
Keywords: rogue waves; order; eighth order; order variable ... See more keywords
Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence
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DOI: 10.1155/2019/1427809
Abstract: The main contribution of this study is to present a new optimal eighth-order scheme for locating zeros with multiplicity . An extensive convergence analysis is presented with the main theorem in order to demonstrate the… read more here.
Keywords: order; eighth order; order convergence; local convergence ... See more keywords
A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics
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DOI: 10.1155/2021/5597186
Abstract: In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the… read more here.
Keywords: eighth order; family optimal; multiple roots; family ... See more keywords
Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber
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DOI: 10.1186/s13662-019-2121-5
Abstract: This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fiber. Starting from the spectral analysis of… read more here.
Keywords: riemann hilbert; equation; nonlinear schr; eighth order ... See more keywords
Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions
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DOI: 10.3390/math6110260
Abstract: The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions… read more here.
Keywords: order; eighth order; ball convergence; convergence efficient ... See more keywords
Convergence Analysis of Weighted-Newton Methods of Optimal Eighth Order in Banach Spaces
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DOI: 10.3390/math7020198
Abstract: We generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study their local convergence. In a previous study, the Taylor expansion of higher order derivatives is employed which may not exist… read more here.
Keywords: newton methods; convergence; order; weighted newton ... See more keywords
An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots
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DOI: 10.3390/math7080672
Abstract: In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity ( m ≥ 1 ) . We use the weight function… read more here.
Keywords: iterative methods; multiple roots; eighth order; family ... See more keywords
Local Convergence of Solvers with Eighth Order Having Weak Conditions
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DOI: 10.3390/sym12010070
Abstract: In particular, the problem of approximating a solution of an equation is of extreme importance in many disciplines, since numerous problems from diverse disciplines reduce to solving such equations. The solutions are found using iterative… read more here.
Keywords: order; solvers eighth; eighth order; convergence solvers ... See more keywords
Fixed-Point Iterative Method with Eighth-Order Constructed by Undetermined Parameter Technique for Solving Nonlinear Systems
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DOI: 10.3390/sym13050863
Abstract: In this manuscript, by using undetermined parameter method, an efficient iterative method with eighth-order is designed to solve nonlinear systems. The new method requires one matrix inversion per iteration, which means that computational cost of… read more here.
Keywords: iterative method; eighth order; undetermined parameter; method ... See more keywords