33.17.3 Adaptive Time Step Settings Dialog Box

The Adaptive Time Step Settings dialog box is used to set the parameters that control the adaptive time stepping. See Section  26.12.2 for details.

Controls

Truncation Error Tolerance   specifies the threshold value to which the computed truncation error is compared. Increasing this value will lead to an increase in the size of the time step and a reduction in the accuracy of the solution. Decreasing it will lead to a reduction in the size of the time step and an increase in the solution accuracy, although the calculation will require more computational time. For most cases, the default value of 0.01 is acceptable.

Ending Time   specifies an ending time for the calculation. Since the ending time cannot be determined by multiplying the number of time steps by a fixed time step size, you need to specify it explicitly.

Minimum/Maximum Time Step Size   specify the upper and lower limits for the size of the time step. If the time step becomes very small, the computational expense may be too high; if the time step becomes very large, the solution accuracy may not be acceptable to you. You can set the limits that are appropriate for your simulation.

Minimum/Maximum Step Change Factor   limit the degree to which the time step size can change at each time step. Limiting the change results in a smoother calculation of the time step size, especially when high-frequency noise is present in the solution. If the time step change factor, $f$, is computed as the ratio between the specified truncation error tolerance and the computed truncation error, the size of time step $\Delta t_n$ is computed as follows:

• If $1 < f < f_{\rm max}$, $\Delta t_n$ is increased to meet the required tolerance.

• If $1 < f_{\rm max} < f$, $\Delta t_n$ is increased, but its maximum possible value is $f_{\rm max}\Delta t_{n-1}$.

• If $f_{\rm min} < f < 1$, $\Delta t_n$ is unchanged.

• If $f < f_{\rm min} < 1$, $\Delta t_n$ is decreased.

Number of Fixed Time Steps   specifies the number of fixed-size time steps that should be performed before the size of the time step starts to change. The size of the fixed time step is the value specified for Time Step Size under Time.

User-Defined Time Step   contains a drop-down list of available user-defined functions.