On a Three-Step Method with the Order of Convergence 1 + 2$$ \sqrt{2} $$ for the Solution of Systems of Nonlinear Operator Equations
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DOI: 10.1007/s10958-017-3279-6
Abstract: We propose a three-step modification of a method with an order of convergence 1+ 2$$ \sqrt{2} $$ aimed at the solution of nonlinear operator equations. We prove that the method is convergent and estimate its… read more here.
Keywords: three step; order convergence; operator equations; nonlinear operator ... 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
The Order of Convergence of Difference Schemes for Fractional Equations
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DOI: 10.1080/01630563.2017.1297825
Abstract: ABSTRACT In this paper, we continue our research on convergence of difference schemes for fractional differential equations. Using implicit difference scheme and explicit difference scheme, we have a deal with the full discretization of the… read more here.
Keywords: schemes fractional; difference; order convergence; convergence difference ... See more keywords
Accelerating order of convergence using secant type methods
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DOI: 10.1080/09720502.2015.1033845
Abstract: Abstract By amalgamating a secant type method and a Newton type method, another method of order 4 has been derived. The method has been supported by examples and has been compared with existing similar methods. read more here.
Keywords: order convergence; secant type; convergence using; type ... See more keywords
Beyond second-order convergence in simulations of magnetized binary neutron stars with realistic microphysics
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DOI: 10.1093/mnras/stz2809
Abstract: We investigate the impact of using high-order numerical methods to study the merger of magnetized neutron stars with finite-temperature microphysics and neutrino cooling in full general relativity. By implementing a fourth-order accurate conservative finite-difference scheme… read more here.
Keywords: order; second order; order convergence; beyond second ... 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