Abstract
In the domain of continuous-time dynamic systems (CTDS), the solution engine associated with a simulation model is generally a suitably selected numerical procedure for solving the ordinary differential equations associated with the so-called initial value problem. Many such procedures exist, each with their own properties, strengths and weaknesses, and some appreciation for the underlying mechanisms is essential. In this regard the Runge–Kutta family and the linear multistep family are outlined together with the related issues of step-size management and error control. Often it is of critical importance to ensure that the procedure selected for use in any particular study is compatible with distinctive features of the differential equations that constitute the simulation model being studied. Issues requiring special attention are outlined, e.g. stability, stiffness and the handling of discontinuities. The chapter concludes with an illustrative example of a modelling and simulation project in the CTDS domain.
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Notes
- 1.
The eigenvalues of the NxN matrix A are the N solutions λ 1, λ 2, …. λ N to the equation det(λ I − A) = 0 where det( ) represents the determinant.
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Birta, L.G., Arbez, G. (2013). Simulation with CTDS Models. In: Modelling and Simulation. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-2783-3_9
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DOI: https://doi.org/10.1007/978-1-4471-2783-3_9
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