Numerical integration and error analysis

Abstract

Integration of rate equations is crucial in dynamic simulation studies. Therefore, a large number of numerical methods has been developed. In general, however, just two methods are sufficient to solve most problems. These are the rectangular integration method of Euler and the method of Runge-Kutta. The former has been explained in Chapter 2, whereas the latter will be introduced in Section 6.2. Integration methods are developed to integrate continuous equations. However, discontinuities may occur, for instance the harvesting of biomass. The actions that are to be taken at such events are treated in Section 6.3. That section also presents a table that helps in selecting an appropriate integration method for a problem. Since in principle in numerical integration it is assumed that rates have a polynomial time trend during the time interval of integration, all numerical integration methods will introduce errors. The severity of these errors and their relation to the ratio of Δt/τ will be discussed in Section 6.4.KeywordsRelative ErrorIntegration MethodExponential CurveIntegration IntervalIntegration ErrorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.