Abstract
In this chapter we describe the use of LMMs to solve systems of ODEs and show how the notion of absolute stability can be generalized to such problems. We begin with an example.
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Bibliography
M. Braun. Differential Equations and their Applications. Springer-Verlag, 1983.
D. J. Higham and L. N. Trefethen. Stiffness of ODEs. BIT Numer. Math., 33:285–303, 1993.
R. K. Nagle, E. B. Saff, and A. D. Snider. Fundamentals of Differential Equations and Boundary Value Problems. Pearson Education Inc., 4th edition, 2004.
R. E. O’Malley, Jr. Thinking About Ordinary Differential Equations, volume 18 of Cambridge Texts in Applied Mathematics. Cambridge University Press, 1997.
L. N. Trefethen and M. Embree. Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press, Princeton, 2005.
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Griffiths, D.F., Higham, D.J. (2010). Linear Multistep Methods—IV: Systems of ODEs. In: Numerical Methods for Ordinary Differential Equations. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-0-85729-148-6_7
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DOI: https://doi.org/10.1007/978-0-85729-148-6_7
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