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Solving boundary value problems in the open source software R: package bvpSolve

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The R package bvpSolve for the numerical solution of Boundary Value Problems (BVPs) is presented. This package is free software which is distributed under the GNU General Public License, as part of the R open source software project. It includes some well known codes to solve boundary value problems of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). In addition to the packages already available for solving initial value problems, the new package now allows non expert users to efficiently solve boundary value problems in the problem solving environment R.
Rocznik
Strony
387--403
Opis fizyczny
Bibliogr. 39 poz., rys., wykr.
Twórcy
autor
  • Universita degli Studi di Bari Dipartimento di Matematica Via Orabona 4, 70125 Bari, Italy
autor
  • Imperial College London South Kensington Campus Department of Mathematics London SW7 2AZ, United Kingdom
autor
  • Royal Netherlands Institute of Sea Research (NIOZ) 4401 NT Yerseke, The Netherlands
Bibliografia
  • [1] U.M. Ascher, J. Christiansen, R.D. Russell, Collocation software for boundary-value ODEs, Acm Trans. Math. Software 7 (1981), 209-222.
  • [2] U.M. Ascher, R.M.M. Mattheij, R.D. Russell, Numerical solution of boundary value problems for ordinary differential equations, vol. 13 of Classics in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995, ISBN 0-89871-354-4. Corrected reprint of the 1988 original.
  • [3] U.M. Ascher, L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, 1998.
  • [4] U.M. Ascher, R.J. Spiteri, Collocation software for boundary value differential-algebraic equations, SIAM J. Sci. Comput. 15 (1994) 4, 938-952.
  • [5] G. Bader, U.M. Ascher, A new basis implementation for a mixed order boundary value ODE solver, SIAM Journal on Scientiffic and Statistical Computing 8 (1987), 483-500.
  • [6] Z. Bashir-Ali, J.R. Cash, H.H.M. Silva, Lobatto deferred correction for stiff two-point boundary value problems, Comput. Math. Appl. 36 (1998) 10-12, 59-69, Advances In difference equations, II.
  • [7] L. Brugnano, F. Mazzia, D. Trigiante, Fifty Years of Stiffness, [in:] Recent Advances in Computational and Applied Mathematics, Springer Science+Business Media B.V., 2011.
  • [8] L. Brugnano, D. Trigiante, On the characterization of stiffness for ODEs, Dynam. Contin. Discrete Impuls. Systems 2 (1996) 3, 317-335.
  • [9] J.R. Cash, Algorithms for the solution of two-point boundary value problems, http://www2.imperial.ac.uk~jcash/BVP_software/readme.php.
  • [10] J.R. Cash, D. Hollevoet, F. Mazzia, A.M. Nagy, Algorithm 927: the MATLAB code bvptwp.m for the numerical solution of two point boundary value problems, ACM Trans.Math. Software 39 (2013) 2, Art. 15, 12.
  • [11] J.R. Cash, F. Mazzia, A new mesh selection algorithm, based on conditioning, for two-point boundary value codes, J. Comput. Appl. Math. 184 (2005) 2, 362-381.
  • [12] J.R. Cash, F. Mazzia, Hybrid mesh selection algorithms based on conditioning for two-point boundary value problems, JNAIAM J. Numer. Anal. Ind. Appl. Math. 1 (1) (2006), 81-90.
  • [13] J.R. Cash, F. Mazzia, Conditioning and hybrid mesh selection algorithms for two-point boundary value problems, Scalable Computing: Practice and Experience 10(4) (2009),347-361.
  • [14] J.R. Cash, G. Moore, R. Wright, An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems, ACM Transaction of Mathematical Software 27 (2) (2001), 245-266.
  • [15] J.R. Cash, M.H. Wright, A deferred correction method for nonlinear two-point boundary value problems: implementation and numerical evaluation., SIAM J. Sci. Statist. Comput. 12 (4) (1991), 971-989.
  • [16] J.W. Eaton, GNU Octave Manual, Network Theory Limited, 2002, ISBN 0-9541617-2-6.
  • [17] W.E. Enright, P.H. Muir, Runge-Kutta software with defect control for boundary value odes, SIAM J. Sci. Comput. 17 (1996), 479-497.
  • [18] W.H. Enright, P.H. Muir, Effcient classes of Runge-Kutta methods for two-point boundary value problems, Computing 37 (4) (1986), 315-334.
  • [19] E. Hairer, S.P. Norsett, G. Wanner, Solving Ordinary Differential Equations I: Nonsti_Problems. 2nd revised ed., Springer-Verlag, Heidelberg, 2009.
  • [20] E. Hairer, G. Wanner, Solving Ordinary Differential Equations II: Stiff andDifferential-Algebraic Problems., Springer-Verlag, Heidelberg, 1996.
  • [21] F. Iavernaro, F. Mazzia, D. Trigiante, Stability and conditioning in numerical analysis,JNAIAM J. Numer. Anal. Ind. Appl. Math. 1 (1) (2006), 91-112.
  • [22] The Mathworks, Matlab release 2011b.
  • [23] F. Mazzia, A.M. Nagy, Stiffness detection strategy for explicit Runge Kutta methods,AIP Conference Proceedings 1281 (2010) 1, 239-242.
  • [24] F. Mazzia, A. Sestini, D. Trigiante, B-spline linear multistep methods and their continuous extensions, SIAM J. Numer. Anal. 44 (2006) 5, 1954-1973 (electronic).
  • [25] F. Mazzia, A. Sestini, D. Trigiante., The continous extension of the B-spline linear multistep metods for BVPs on non-uniform meshes., Appl. Numer. Math. 59 (2009)3{4, 723-738.
  • [26] F. Mazzia, D. Trigiante, A hybrid mesh selection strategy based on conditioning for boundary value ODE problems, Numer. Algorithms 36 (2004) 2, 169-187.
  • [27] F. Mazzia, D. Trigiante, E_cient strategies for solving nonlinear problems in BVPs codes, Nonlinear Stud. 17 (2010) 4, 309-326.
  • [28] M.B. Monagan, K.O. Geddes, K.M. Heal, G. Labahn, S.M. Vorkoetter, J. McCarron, P. DeMarco, Maple 10 Programming Guide, Maplesoft, Waterloo ON, Canada, 2005.
  • [29] R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2011.
  • [30] Scilab Consortium, Scilab: The free software for numerical computation, Scilab Consor- tium, Digiteo, Paris, France, 2011.
  • [31] K. Soetaert, rootSolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations, 2009. R package version 1.6.
  • [32] K. Soetaert, J.R. Cash, F. Mazzia, Solving Differential Equations in R, Springer, 2012, ISBN 978-3-642-28069-6.
  • [33] K. Soetaert, J.R. Cash, F. Mazzia, bvpSolve: Solvers for Boundary Value Problems of Ordinary Differential Equations, 2013, R package version 1.2.4.
  • [34] K. Soetaert, J.R. Cash, F. Mazzia, deTestSet: Testset for differential equations, 2013, R package version 1.1.1.
  • [35] K. Soetaert, F. Meysman, Reactive transport in aquatic ecosystems: Rapid model prototyping in the open source software R, Environmental Modelling and Software, in press, (2011).
  • [36] K. Soetaert, T. Petzoldt, R.W. Setzer, R-package deSolve, Writing Code in Compiled Languages, 2009, Package vignette.
  • [37] K. Soetaert, T. Petzoldt, R.W. Setzer, Solving differential equations in R: Package deSolve, Journal of Statistical Software 33 (2010) 9, 1-25.
  • [38] S. Theu_l, A. Zeileis, Collaborative Software Development Using R-Forge, The R Journal 1 (2009) 1, 9-14.
  • [39] I. Wolfram Research, Mathematica Edition, Version 8.0, Wolfram Research Inc., 2010.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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