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2 - Stability Analysis of ODE Integrators

Published online by Cambridge University Press:  05 May 2016

Graham W. Griffiths
Affiliation:
City University London
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Summary

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Type
Chapter
Information
Numerical Analysis Using R
Solutions to ODEs and PDEs
, pp. 74 - 101
Publisher: Cambridge University Press
Print publication year: 2016

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References

[But-07] Butcher, J. (2007), Runge-Kutta Methods, Scholarpedia 2–9, 3147. Available online at http://www.scholarpedia.org/article/Runge-Kutta_methods.Google Scholar
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[Dah-75] Dahlquist, G. (1975), Error Analysis for a Class of Methods for Stiff Nonlinear Initial Value Problems, Procs. Numerical Analysis Conference, Dundee, Lecture Notes in Math. 506, G.A., Watson (ed.), Springer Verlag, 1976, pp. 60–74.Google Scholar
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[Gea-71] Gear, C.W. (1971), Numerical Initial Value Problems inOrdinaryDifferential Equations, Prentice Hall.
[Goe-14] Goedman, G., and G., Grothendieck (2014), R Interface to the yacas Computer Algebra System Ryacas. Available online at http://cran.r-project.org/web/packages/Ryacas/ Ryacas.pdf.
[Lam-91] Lambert, J. D. (1991), Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, JohnWiley.
[Ric-71] Richtmyer, R.D. and K.W., Morton (1967), Difference Methods for Initial-Value Problems, 2nd ed., JohnWiley.
[Sha-94] Shampine, L.F. (1994), Numerical Solution ofOrdinaryDifferential Equations, Chapman Hall.
[Sha-97] Shampine, L. F. and M. W., Reichelt (1997), a. SIAM Journal on Scientific Computing 1–18, 1–22.
[Sch-91] Schiesser, W. E. (1991), TheNumericalMethod of Lines: Integration of PartialDifferential Equations, Academic Press.
[Som-94] Sommeijer, B. P., P. J. van der, Houwen and J., Kok (1994), Time Integration of Three- Dimensional Numerical TransportModels, Applied NumericalMathematics 16, 201–225.
[Wes-01] Wesseling, P. (2001), Principles of Computational Fluid Dynamics, Springer.

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