dae
Status: planned (wave 3). No code exists. The package name is provisional, and so is the home: the bibliography leaves open whether the solver lives here or in go-numerics/integrate, which has stiff ODE solvers (Radau, BDF) and event handling but no DAE support and no mass matrix.
What it will provide
- Index-1 systems in fully implicit form, F(t, y, y’) = 0, by a variable-order, variable-step BDF method (DASSL and IDA).
- Semi-explicit systems M y’ = f and mass-matrix problems, through Radau IIA.
- Consistent initial conditions.
- Events: zero crossings and discontinuities, restarting on dense output.
Without an expression system, only index-1 systems and user-supplied reduced
systems are feasible; index reduction belongs to model.
References
| Subject | Reference |
|---|---|
| DAE, BDF | Brenan, Campbell and Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM 1996, doi:10.1137/1.9781611971224; Petzold, SIAM J. Sci. Stat. Comput. 4(1), 1983, doi:10.1137/0904010 |
| Radau, mass matrix | Hairer and Wanner, Solving Ordinary Differential Equations II, 2nd ed., Springer 1996, doi:10.1007/978-3-642-05221-7 |
| consistent initial conditions | Brown, Hindmarsh and Petzold, SIAM J. Sci. Comput. 19(5), 1998, doi:10.1137/S1064827595289996 |
How it will be validated
| Area | Criterion |
|---|---|
| DAE | error against the reference solution of the Bari test set at a stated tolerance; index-1 constraint residual; final-time error, constraint drift, steps, Newton iterations; event times to 1e-10 |
Reference implementations: SUNDIALS (IDA, BSD-3-Clause), DASSL from netlib (SLATEC, public domain) and Hairer’s RADAU5 (BSD-2-style licence). The Bari Test Set for IVP Solvers is the corpus; its licence is unspecified, so the cases are generated and cited, never redistributed. Every item also needs unit tests at 100% coverage and a performance table against the reference.
Created on by tannevaled
Modified on by tannevaled