27.7 References and Further Reading
- Ascher, U.M., Petzold, L.R., Computer Methods for Ordinary
Differential and Differential-Algebraic Equations, SIAM,
- Hairer, E., Norsett, S. P., Wanner, G., Solving Ordinary Differential
Equations I: Nonstiff Problems, Springer, Berlin, 1993.
- Hairer, E., Wanner, G., Solving Ordinary Differential
Equations II: Stiff and Differential-Algebraic Problems,
Springer, Berlin, 1996.
Many of the basic Runge-Kutta formulas can be found in the Handbook of
- Abramowitz & Stegun (eds.), Handbook of Mathematical Functions,
The implicit Bulirsch-Stoer algorithm
bsimp is described in the
- G. Bader and P. Deuflhard, “A Semi-Implicit Mid-Point Rule for Stiff
Systems of Ordinary Differential Equations.”, Numer. Math. 41, 373–398,
The Adams and BDF multistep methods
are based on the following articles,
- 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.
- P. N. Brown, G. D. Byrne and A. C. Hindmarsh, “VODE: A
Variable-coefficient ODE Solver.”, SIAM J. Sci. Stat. Comput. 10,
- 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.