×

zbMATH — the first resource for mathematics

Nonnegative solutions of ODEs. (English) Zbl 1082.65547
Summary: This paper discusses procedures for enforcing nonnegativity in a range of codes for solving ordinary differential equations (ODEs). The codes implement both one-step and multistep methods, all of which use continuous extensions and have event finding capabilities. Examples are given.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ()
[2] Brenan, K.E.; Campbell, S.L.; Petzold, L.R., Numerical solution of initial-value problems in differential-algebraic equations, SIAM classics in applied mathematics, vol. 14, (1996), SIAM Philadelphia · Zbl 0844.65058
[3] Brown, P.N.; Byrne, G.D.; Hindmarsh, A.C., VODE: A variable-coefficient ODE solver, SIAM J. sci. stat. comput., 10, 1038-1051, (1989) · Zbl 0677.65075
[4] Buzzi Ferraris, G.; Manca, D., Bzzode: a new C++ class of stiff and non-stiff ordinary differential equation systems, Comput. chem. eng., 22, 1595-1621, (1998)
[5] G.D. Byrne, S. Thompson, A.C. Hindmarsh, VODE_F90: A Fortran 90 revision of VODE with added features, work in progress.
[6] Dahlquist, G.; Edsberg, L.; Sköllermo, G.; Söderlind, G., Are the numerical methods and software satisfactory for chemical kinetics?, (), 149-164
[7] Edsberg, L., Numerical methods for mass action kinetics, (), 181-195
[8] Enright, W.H.; Hull, T.E., Comparing numerical methods for the solution of stiff systems of ODEs arising in chemistry, (), 48-66 · Zbl 0301.65040
[9] Hindmarsh, A.C.; Byrne, G.D., Applications of EPISODE: an experimental package for the integration of systems of ordinary differential equations, (), 147-166
[10] G.R. Huxel, Private communication, Biology Dept., Univ. of South Florida, Tampa, FL, 2004.
[11] I. Karasalo, J. Kurylo, On solving the stiff ODEs of the kinetics of chemically reacting gas flow, Lawrence Berkeley Lab. Rept., Berkeley, CA, 1979. · Zbl 0468.76095
[12] {\scMatlab}, The MathWorks, Inc., 3 Apple Hill Dr., Natick, MA 01760, 2004.
[13] W.E. Schiesser, Private communication, Math. and Engr., Lehigh Univ., Bethlehem, PA, 2004.
[14] Schiesser, W.E., Computational mathematics in engineering and applied science: ODEs, DAEs, and pdes, (1994), CRC Press Boca Raton · Zbl 0857.65083
[15] Shampine, L.F., Conservation laws and the numerical solution of odes, Comp. math. appl., 12B, 1287-1296, (1986) · Zbl 0641.65057
[16] Shampine, L.F., Conservation laws and the numerical solution of ODEs, II, Comp. math. appl., 38, 61-72, (1999) · Zbl 0947.65086
[17] Shampine, L.F., Numerical solution of ordinary differential equations, (1994), Chapman & Hall New York · Zbl 0826.65082
[18] Shampine, L.F.; Hosea, M.E., Analysis and implementation of TR-BDF2, Appl. numer. math., 20, 21-37, (1996) · Zbl 0859.65076
[19] Shampine, L.F.; Reichelt, M.W., The {\scmatlab} ODE suite, SIAM J. sci. comput., 18, 1-22, (1997) · Zbl 0868.65040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.