# Absolute tolerance

Absolute tolerance for solver tolerance calculation

Model Configuration Pane: Solver

## Description

Specify the largest acceptable solver error as the value of the measured state approaches zero.

At each time step, the solver:

• Calculates the value of each state

• Estimates the error in each state calculation

• Determines the acceptable error for each state using the relative tolerance, absolute tolerance, and state values

The acceptable error considered for each state on each time step is determined by either the relative tolerance or the absolute tolerance, whichever results in a larger tolerance. The solver calculates the acceptable error based on the relative tolerance by multiplying the relative tolerance and the state value.

ei = reltol * |x|,

where:

• ei is the acceptable error based on relative tolerance at that time step.

• reltol is the value specified for the Relative tolerance parameter.

• x is the state value.

When ei is larger than the value specified for the Absolute tolerance parameter, the relative tolerance determines the tolerance for that state on that time step. When the absolute tolerance is greater than ei, the absolute tolerance determines the tolerance for that state on that time step. In general, the absolute tolerance applies when the state values approach zero.

For more information, see Error Tolerances for Variable-Step Solvers.

## Dependencies

To enable this parameter:

• Set the solver Type to `Variable-step`.

• Set the Solver parameter to a value other than `discrete (no continuous states)`.

## Settings

`auto` | positive scalar number

By default, the value is `auto`, and the software scales the value of the absolute tolerance based on the state values during simulation. The software determines the initial absolute tolerance based on the value of the relative tolerance.

abstol = reltol * 1e-3 when reltol ≤ 1e-3

abstol = 1e-6 when reltol > 1e-3,

where abstol is the absolute tolerance and reltol is the relative tolerance.

As the simulation progresses, the absolute tolerance for each state is scaled to the maximum value that state has reached up to the current time step times the relative tolerance.

abstol = xmax * reltol

For example, if a state reaches a value of `1` during the simulation and the relative tolerance is `1e-4`, the absolute tolerance is initialized to `1e-7` and reaches a value of `1e-4` by the end of the simulation.

When you specify the absolute tolerance as a positive scalar number, you can choose whether to scale the absolute tolerance based on state values during simulation using the Auto scale absolute tolerance parameter.

## Tips

• Some blocks have a block parameter that allows you to specify an absolute tolerance value for the software to use when computing the acceptable error for those block states. When you specify a value for the block parameter, the software uses the block parameter value instead of the model configuration parameter value when calculating acceptable state errors for states of that block. Such blocks include:

Consider specifying the block parameter value when the states in your model vary widely in magnitude.

• If your simulation results do not seem accurate, and if your model has states with values that approach zero, then the absolute tolerance might be too large.

• Specifying a small absolute tolerance might slow the simulation because the solver might take more steps than necessary near time points where the state values are near zero.

• To check the accuracy of a simulation, you can reduce the absolute tolerance and simulate the model again. If the results of the two simulations are not significantly different, then the solution has converged.

## Recommended Settings

The table summarizes recommended values for this parameter based on considerations related to code generation.

ApplicationSetting
DebuggingNo impact
TraceabilityNo impact
EfficiencyNo impact
Safety precautionNo impact

## Programmatic Use

 Parameter: `AbsTol` Type: string | character vector Value: `'auto'` | positive scalar number Default: `'auto'`

## Version History

Introduced before R2006a