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

A family of modified Ostrowski’s methods with optimal eighth order of convergence

Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. Numerical comparisons are made with other existing second- and fourth-order schemes to solve the nonlinear system of equations of the Global Positioning System and some academic nonlinear systems.

/pdf/fourth-and-fifth-order-methods-for-solving-nonlinear-systems-2px3imh18a.pdf

Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System

On interpolation variants of Newton's method for functions of several variables

Semilocal convergence by using recurrence relations for a fifth-order method in Banach spaces

The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package MATHEMATICA provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.

/pdf/basins-of-attraction-for-various-steffensen-type-methods-29yivnbb4u.pdf

Alicia Cordero

Papers

A family of modified Ostrowski’s methods with optimal eighth order of convergence

Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System

On interpolation variants of Newton's method for functions of several variables

Semilocal convergence by using recurrence relations for a fifth-order method in Banach spaces

Basins of Attraction for Various Steffensen-Type Methods