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

Optimal iterative methods for finding multiple roots of nonlinear equations using weight functions and dynamics

A family of derivative-free methods of seventh-order
convergence for solving nonlinear equations is suggested. In the proposed
methods, several linear combinations of divided differences are used in
order to get a good estimation of the derivative of the given function at
the different steps of the iteration. The efficiency indices of the members of
this family are equal to 1.6266. Also, numerical examples are used to show
the performance of the presented methods, on smooth and nonsmooth
equations, and to compare with other derivative-free methods, including
some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.

/pdf/a-family-of-derivative-free-methods-with-high-order-of-4laj6cehsw.pdf

A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

Technological advances of XXth century have induced a profound change in society and, therefore, in the high education. Internet supposed a qualitative difference, as information and digital images flooded into homes around the world. The Universitat Polite`cnica de Vale`ncia (UPV) is a medium sized university of Spain that has been involved in the development of digital video content (Polimedia) to support teaching processes for several years. Joint with Polimedia and other learning objects (virtual laboratories, applets, etc.), the UPV promoted the construction of OCWs. Along with the improvement of technology, MOOCs appeared as e-learning material. In this work, we analyze the advantages and drawbacks of OCWs and MOOCs when they are used in our classroom. This experience has led us to incorporate in our methodology the flip teaching.

/pdf/towards-a-better-learning-models-through-ocws-and-moocs-3dubdldhlu.pdf

Alicia Cordero

Papers

Optimal iterative methods for finding multiple roots of nonlinear equations using weight functions and dynamics

A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

Towards a better learning models through OCWs and MOOCs

One-point Newton-type iterative methods

On the convergence of a higher order family of methods and its dynamics