# OALTS

Optimal A-stable Linear Two-Step Method

References:

1. [10.1002/nme.6188](https://doi.org/10.1002/nme.6188)
2. [10.1002/nme.6623](https://doi.org/10.1002/nme.6623)

## Syntax

```
integrator OALTS (1) [2]
# (1) int, unique integrator tag
# [2] double, spectral radius, default: 0.5
```

## Remarks

This method is closely related to the [Generalised-Alpha](generalizedalpha) method (on first order ODEs).\
See the second reference for more details, also see [10.1016/j.compstruc.2017.08.013](https://doi.org/10.1016/j.compstruc.2017.08.013).

This method requires a fixed time step.\
The initial time step is used for time marching.\
For example,

```
set ini_step_size 1E-2
```

The `fixed_step_size` command such as

```
set fixed_step_size true
```

is not required and this flag is always `true`.

## Accuracy Analysis

![oalts-0.0](https://4006314410-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MQ5rMqEBbzA9NgGETGX%2Fuploads%2Fgit-blob-7864b123c4cc443ddcc9b50457a36413347b24d4%2Foalts-0.0.svg?alt=media) ![oalts-0.5](https://4006314410-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MQ5rMqEBbzA9NgGETGX%2Fuploads%2Fgit-blob-99abd5cd51a25397e0615fb45a4447c53bdc6b1c%2Foalts-0.5.svg?alt=media) ![oalts-1.0](https://4006314410-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MQ5rMqEBbzA9NgGETGX%2Fuploads%2Fgit-blob-99906ab229d69789e4434fcb5dea57cd5bab3977%2Foalts-1.0.svg?alt=media)
