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Previous: <a href="ODE-Example-programs.html#ODE-Example-programs" accesskey="p" rel="previous">ODE Example programs</a>, Up: <a href="Ordinary-Differential-Equations.html#Ordinary-Differential-Equations" accesskey="u" rel="up">Ordinary Differential Equations</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="References-and-Further-Reading-19"></a>
<h3 class="section">27.7 References and Further Reading</h3>
<ul class="no-bullet">
<li><!-- /@w --> Ascher, U.M., Petzold, L.R., <cite>Computer Methods for Ordinary
Differential and Differential-Algebraic Equations</cite>, SIAM,
Philadelphia, 1998.
</li></ul>
<ul class="no-bullet">
<li><!-- /@w --> Hairer, E., Norsett, S. P., Wanner, G., <cite>Solving Ordinary Differential
Equations I: Nonstiff Problems</cite>, Springer, Berlin, 1993.
</li></ul>
<ul class="no-bullet">
<li><!-- /@w --> Hairer, E., Wanner, G., <cite>Solving Ordinary Differential
Equations II: Stiff and Differential-Algebraic Problems</cite>,
Springer, Berlin, 1996.
</li></ul>
<p>Many of the basic Runge-Kutta formulas can be found in the Handbook of
Mathematical Functions,
</p>
<ul class="no-bullet">
<li><!-- /@w --> Abramowitz & Stegun (eds.), <cite>Handbook of Mathematical Functions</cite>,
Section 25.5.
</li></ul>
<p>The implicit Bulirsch-Stoer algorithm <code>bsimp</code> is described in the
following paper,
</p>
<ul class="no-bullet">
<li><!-- /@w --> G. Bader and P. Deuflhard, “A Semi-Implicit Mid-Point Rule for Stiff
Systems of Ordinary Differential Equations.”, Numer. Math. 41, 373–398,
1983.
</li></ul>
<p>The Adams and BDF multistep methods <code>msadams</code> and <code>msbdf</code>
are based on the following articles,
</p>
<ul class="no-bullet">
<li><!-- /@w --> G. D. Byrne and A. C. Hindmarsh, “A Polyalgorithm for the
Numerical Solution of Ordinary Differential Equations.”,
ACM Trans. Math. Software, 1, 71–96, 1975.
</li><li><!-- /@w --> P. N. Brown, G. D. Byrne and A. C. Hindmarsh, “VODE: A
Variable-coefficient ODE Solver.”, SIAM J. Sci. Stat. Comput. 10,
1038–1051, 1989.
</li><li><!-- /@w --> A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban,
D. E. Shumaker and C. S. Woodward, “SUNDIALS: Suite of
Nonlinear and Differential/Algebraic Equation Solvers.”, ACM
Trans. Math. Software 31, 363–396, 2005.
</li></ul>
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