# DynamicBoundspODEsDiscrete.jl

Parametric Discretize-and-Relax methods within DynamicBounds.jl

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## Summary

This package implements a discretize-and-relax approaches to computing state bounds and relaxations using the DynamicBounds.jl framework. These methods discretize the time domain over into a finite number of points and then compute valid relaxations at these time-points. Full documentation of this functionality may be found here in the DynamicBounds.jl website.

## Installation

using Pkg; Pkg.add("DynamicBoundspODEsDiscrete")

or using the following command in the package manager environment

```
pkg > add DynamicBoundspODEsDiscrete
```

Note that this package can also be used directly via DynamicBounds.jl as the later package automatically reexports it.

## References

- Corliss, G. F., & Rihm, R. (1996). Validating an a priori enclosure using high-order Taylor series. MATHEMATICAL RESEARCH, 90, 228-238.
- Lohner, R. J. (1992, January). Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems. In Institute of mathematics and its applications conference series (Vol. 39, pp. 425-425). Oxford University Press.
- Nedialkov, Nedialko S., and Kenneth R. Jackson. "An interval Hermite-Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation." Reliable Computing 5.3 (1999): 289-310.
- Nedialkov, Nedialko Stoyanov. Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation. University of Toronto, 2000.
- Nedialkov, N. S., & Jackson, K. R. (2000). ODE software that computes guaranteed bounds on the solution. In Advances in Software Tools for Scientific Computing (pp. 197-224). Springer, Berlin, Heidelberg.
- Sahlodin, A. M., & Chachuat, B. (2011). Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs. Applied Numerical Mathematics, 61(7), 803-820.
- Wilhelm, M. E., Le, A. V., & Stuber, M. D. (2019). Global optimization of stiff dynamical systems. AIChE Journal, 65(12), e16836