This is an old version, view current version.

16.2 Example: chemical kinetics

As an example of a system of DAEs, consider following chemical kinetics problem(Robertson 1966). The nondimensionalized DAE consists of two differential equations and one algebraic constraint. The differential equations describe the reactions from reactants y1 and y2 to the product y3, and the algebraic equation describes the mass conservation. (Serban and Hindmarsh 2021).

dy1dt+αy1βy2y3=0dy2dtαy1+βy2y3+γy22=0y1+y2+y31.0=0

The state equations implicitly defines the state (y1(t),y2(t),y3(t)) at future times as a function of an initial state and the system parameters, in this example the reaction rate coefficients (α,β,γ).

Unlike solving ODEs, solving DAEs requires a consistent initial condition. That is, one must specify both y(t0) and y(t0) so that residual function becomes zero at initial time t0 r(y(t0),y(t0),t0)=0

References

Robertson, H. H. 1966. “The Solution of a Set of Reaction Rate Equations.” In Numerical Analysis, an Introduction, 178–82. Lodon; New York: Academic Press.
Serban, Radu, and Alan C. Hindmarsh. 2021. “Example Programs for IDAS.” LLNL-TR-437091. Lawrence Livermore National Laboratory.