Applications of higher-order optimal Newton secant iterative methods in ocean acidification and investigation of long-run implications of emissions on alkalinity of seawater

The Newton secant method is a third-order iterative nonlinear solver. It requires two function and one first derivative evaluations. However, it is not optimal as it does not satisfy the Kung-Traub ...

[1]  R. Bacastow,et al.  Atmospheric carbon dioxide and radiocarbon in the natural carbon cycle: II. Changes from A. D. 1700 to 2070 as deduced from a geochemical model. , 1973, Brookhaven symposia in biology.

[2]  Corinne Le Quéré,et al.  Climate Change 2013: The Physical Science Basis , 2013 .

[3]  J. Traub Iterative Methods for the Solution of Equations , 1982 .

[4]  W. Marsden I and J , 2012 .

[5]  R. A. Walt,et al.  The numerical solution of algebraic equations , 1979 .

[6]  D. Hendry,et al.  Co-Integration and Error Correction : Representation , Estimation , and Testing , 2007 .

[7]  Donggyu Sul,et al.  Cointegration Vector Estimation by Panel Dols and Long-Run Money Demand , 2002 .

[8]  R. F. King A Family of Fourth Order Methods for Nonlinear Equations , 1973 .

[9]  Peter C. B. Phillips,et al.  Statistical Inference in Instrumental Variables Regression with I(1) Processes , 1990 .

[10]  D. K. R. Babajee,et al.  On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations , 2012, Int. J. Math. Math. Sci..

[11]  B. Kalantari Polynomial Root-finding and Polynomiography , 2008 .

[12]  M. Z. Dauhoo,et al.  An analysis of the properties of the variants of Newton's method with third order convergence , 2006, Appl. Math. Comput..

[13]  K. Caldeira,et al.  Oceanography: Anthropogenic carbon and ocean pH , 2003, Nature.

[14]  A. Householder Solution of Equations and Systems of Equations (A. M. Ostrowski) , 1967 .

[15]  Walter Vandaele,et al.  Applied Time Series and Box-Jenkins Models , 1983 .

[16]  Tom S. Garrison,et al.  Oceanography: An Invitation to Marine Science , 1993 .

[17]  A. Kanioura,et al.  Critical values for an F-test for cointegration in a multivariate model , 2005 .

[18]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[19]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[20]  J. Durbin,et al.  Testing for serial correlation in least squares regression. II. , 1950, Biometrika.

[21]  E. Maier‐Reimer,et al.  Anthropogenic ocean acidification over the twenty-first century and its impact on calcifying organisms , 2005, Nature.

[22]  Kimio Hanawa,et al.  Observations: Oceanic Climate Change and Sea Level , 2007 .

[23]  J. Stock,et al.  Testing for Common Trends , 1988 .

[24]  H. T. Kung,et al.  Optimal Order of One-Point and Multipoint Iteration , 1974, JACM.

[25]  J. Stock,et al.  Efficient Tests for an Autoregressive Unit Root , 1992 .

[26]  S. Johansen STATISTICAL ANALYSIS OF COINTEGRATION VECTORS , 1988 .

[27]  R. Engle,et al.  COINTEGRATION AND ERROR CORRECTION: REPRESENTATION , 1987 .

[28]  J. Durbin,et al.  Testing for serial correlation in least squares regression. I. , 1950, Biometrika.

[29]  A. B. Kasturiarachi,et al.  Leap-frogging Newton's method , 2002 .

[30]  Edward R Vrscay Julia sets and mandelbrot-like sets associated with higher order Schro¨der rational iteration functions: A computer assisted study , 1986 .

[31]  J. Ries,et al.  Marine calcifiers exhibit mixed responses to CO2-induced ocean acidification , 2009 .