27.7 References and Further Reading

• Ascher, U.M., Petzold, L.R., Computer Methods for Ordinary Differential and Differential-Algebraic Equations, SIAM, Philadelphia, 1998.

• 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 Mathematical Functions,

• Abramowitz & Stegun (eds.), Handbook of Mathematical Functions, Section 25.5.

The implicit Bulirsch-Stoer algorithm bsimp is described in the following paper,

• G. Bader and P. Deuflhard, “A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations.”, Numer. Math. 41, 373–398, 1983.

The Adams and BDF multistep methods msadams and msbdf 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, 1038–1051, 1989.
• 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.