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Evaluation of numerical techniques applied to soil solution speciation including cation exchange
Author(s) -
Vaughan Peter J.
Publication year - 2002
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj2002.4740
Subject(s) - convergence (economics) , simplex , rate of convergence , mathematics , genetic algorithm , cation exchange capacity , nonlinear system , ion exchange , set (abstract data type) , quadratic equation , soil water , chemistry , ion , computer science , physics , soil science , geology , combinatorics , channel (broadcasting) , economic growth , computer network , biology , geometry , quantum mechanics , evolutionary biology , programming language , organic chemistry , economics
Most existing models of soil solution speciation utilize either Newton–Raphson or Picard iteration to obtain a numerical solution to the nonlinear set of algebraic equations expressing mole balance and charge balance of free ions for major species as well as cation exchange. A computer program was written to test speed and accuracy of these and other methods. Picard iteration was fastest but produced a mean relative error (MRE) for mole and charge balance of 0.03 with no further convergence after a few iterations. A tensor (quadratic) method and two simplex methods converged to the correct result. The tensor method was preferable because the final result was more accurate; the rate of convergence was faster by 10 to 100 times, and convergence occurred for all compositions tested up to an ionic strength of 0.25. These results point out the value of testing various algorithms prior to implementation of speciation code applied to soils.