The default methods in COPASI for time course calculations are LSODA and LSODAR [Petzold83]. Both of these methods are part of the ODEPACK library [Hindmarsh83]. LSODA, developed by Linda R. Petzold and Alan C. Hindmarsh, is capable of solving systems of the form $\frac{dy}{dt} = f(t, y)$ using either a dense or banded Jacobian when the system is stiff. Notably, LSODA automatically selects between non-stiff (Adams) and stiff (BDF) integration methods. By default, it begins with the non-stiff algorithm and dynamically tracks the system to determine if and when to switch to the stiff method. LSODAR extends LSODA by adding root-finding capabilities, enabling the accurate detection of the exact time when events occur. COPASI automatically chooses the appropriate method based on the problem at hand.
Integrate Reduced Model
This boolean parameter specifies whether integration should use mass
conservation laws (thereby reducing the number of system variables) or
the complete model. When checked (true), this tells COPASI to utilize
mass conservation laws. Otherwise (false) COPASI will determine all
variables directly from the ODEs.
Relative Tolerance This numeric parameter defines the desired relative tolerance for the simulation. Smaller values result in a more accurate trajectory. The default value is $1.0 \cdot 10^{-6}$. The smallest achievable relative tolerance is approximately $2.22 \cdot 10^{-16}$.
Absolute Tolerance A positive numeric value that sets the desired absolute tolerance. For chemical species, this tolerance applies to concentration values. The default is $1.0 \cdot 10^{-12}$.
Max Internal Steps
A positive integer indicating the maximum number of internal steps the
integrator can perform before the next output time. The default is
10000.
Max Internal Step Size
A positive floating-point value that limits the maximum size of an
internal integration step. The default value is 0, which means no
limit is enforced.
In addition to LSODA, COPASI provides the option to integrate systems of ODEs using the Radau5 integrator. Radau5 is especially well-suited for stiff systems, as it is an implicit Runge-Kutta method of order 5. This integrator is part of the library developed by Ernst Hairer Hairer, E., & Wanner, G. (1996). Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (Vol. 14). Springer.. Note, however, that Radau5 does not support the simulation of events.
Integrate Reduced Model
This boolean parameter determines whether integration should use mass
conservation laws (thus reducing the number of system variables) or use
the complete model. When set to true (the default), COPASI applies
mass conservation laws. When set to false, COPASI determines all
variables directly from the ODEs.
Relative Tolerance Specifies the relative tolerance for the simulation as a numeric value. Lower values increase the accuracy of the calculated trajectory. The default value is $1.0 \cdot 10^{-4}$.
Absolute Tolerance A positive numeric value specifying the absolute tolerance for the simulation. For species, this tolerance is applied to concentration values. The default value is $1.0 \cdot 10^{-6}$.
Max Internal Steps
A positive integer indicating the maximum number of internal steps the
integrator is allowed to take before the next output time. The default
value is 1000000000.
Initial Step Size
A positive floating-point value specifying the initial size of internal
integration steps. The default value is 0.001.
