高等学校計算数学学報 = Numerical mathematics

Marine Carbon BiogeochemistryBiogeochemical Cycles and ClimateGlobal Biogeochemical Cycles in the Climate SystemOcean Dynamics and the Carbon CycleLive Long and EvolveBiogeochemistry of Marine Dissolved Organic MatterOcean Biogeochemical DynamicsMarine Ecosystems and Global ChangeBiological OceanographyNitrogen in the SeaBiogeochemistry of EstuariesInteractions of C, N, P and S Biogeochemical Cycles and Global ChangeGlobal EnvironmentComputational Science — ICCS 2004The Oceans and ClimateMarine Microbiome and Biogeochemical Cycles in Marine Productive AreasMetal Ions in Biological Systems, Volume 43 Biogeochemical Cycles of ElementsNitrogen in the Marine EnvironmentIntroduction to Marine BiogeochemistryOcean Circulation and ClimatePrimary Productivity and Biogeochemical Cycles in the SeaThe Biogeochemical Cycle of Silicon in the OceanChemical OceanographyTowards a Model of Ocean Biogeochemical ProcessesOcean Dynamics and the Carbon CycleOcean BiogeochemistryParticle Analysis in OceanographyBiogeochemical CyclesBiogeochemical Dynamics at Major River-Coastal InterfacesThe Ocean Carbon Cycle and ClimateSensitivity of global ocean biogeochemical dynamics to ecosystem structure in a future climateModeling Methods for Marine ScienceAn Introduction to the Chemistry of the SeaEncyclopedia of Ocean SciencesCO2 in Seawater: Equilibrium, Kinetics, IsotopesThe Biogeochemical Cycle of Silicon in the OceanKuroshio CurrentThe Mediterranean Sea in the Era of Global Change 1Ocean Biogeochemical DynamicsOcean Mixing

Ocean Biogeochemical Dynamics

Variants of Newton’s Method using fifth-order quadrature formulas☆

Different anomalies in a Jarratt family of iterative root-finding methods☆

A reduced composition technique has been used on Newton and Jarratt’s methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations. Following this aim, a family of methods is obtained whose efficiency indices are proved to be better for systems of nonlinear equations.

A modified Newton-Jarratt’s composition

The study of the dynamical behaviour of the operators defined by iterative methods help us to know more deeply the regions where these methods have a good performance. In this paper, we follow the dynamical study of a multipoint variant of the known Chebyshev-Halley's family, showing the existence of attractive periodic orbits of period 2 for some values of the parameter.

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Orbits of period two in the family of a multipoint variant of Chebyshev-Halley family

Design and multidimensional extension of iterative methods for solving nonlinear problems

On the convergence of a damped Newton-like method with modified right hand side vector

A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics

A class of optimal iterative methods for solving nonlinear equations is extended up to sixteenth-order of convergence. We design them by using the weight function technique, with functions of three variables. Some numerical tests are made in order to confirm the theoretical results and to compare the new methods with other known ones.

/pdf/optimal-high-order-methods-for-solving-nonlinear-equations-181canzmgc.pdf

Alicia Cordero

Papers

Orbits of period two in the family of a multipoint variant of Chebyshev-Halley family

Design and multidimensional extension of iterative methods for solving nonlinear problems

On the convergence of a damped Newton-like method with modified right hand side vector

A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics

Optimal High-Order Methods for Solving Nonlinear Equations