User Manual | Methods | Time Course Calculation | Deterministic Simulation

# Deterministic Simulation

### Deterministic (LSODA or LSODAR)

The default methods in COPASI to calculate a time course are LSODA or LSODAR [ Petzold83]. Both methods are part of the ODEPACK library [ Hindmarsh83]. LSODA was written by Linda R. Petzold and Alan C. Hindmarsh.It solves systems $\frac{dy}{dt} = f(t, y)$ with a dense or banded Jacobian when the problem is stiff, but it automatically selects between non-stiff (Adams) and stiff (BDF) methods. It uses the non-stiff method initially, and dynamically monitors data in order to decide which method to use. LSODAR adds root finding capabilities to LSODA which are used to detect the exact location in time when events occur. COPASI automatically chooses the apropriate method for any given problem.

#### Options for LSODA

Integrate Reduced Model
This parameter is a boolean value to determine whether the integration shall be performed using the mass conservation laws, i.e., reducing the number of system variables or to use the complete model. A value of '1' (the default) instructs COPASI to make use of the mass conservation laws, whereas a value of '0' instructs COPASI to determine all variables through ODEs.
Relative Tolerance
This parameter is a numeric value specifying the desired relative tolerance the user wants to achieve. A smaller value means that the trajectory is calculated more accurate. The default value is $1.0 \cdot 10^{-6}$. Please note that best achievable relative tolerance is $2.22 \cdot 10^{-16}$ approximately.
Absolute Tolerance
This parameter is a positive numeric value specifying the desired absolute tolerance the user wants to achieve. Please note that for species the absolute tolerance is applied to the concentration value. The default value is $1.0 \cdot 10^{-12}$.
Max Internal Steps
This parameter is a positive integer value specifying the maximal number of internal steps the integrator is allowed to take before the next desired reporting time. The default value is '10000'.
Max Internal Step Size
This parameter is a positive double value specifying the maximal size of an internal steps the integrator is allowed to take. The default '0' means that there is no such limit.