Tempus tutorials demonstrating its capabilities.
Progression Tutorial
The progression tutorials use the van der Pol problem to introduce Tempus capabilities in a stepwise manner. Starting from a simple application with a hand-written Forward Euler loop, the examples progressively introduce core Tempus and Trilinos abstractions. Each example is runnable on its own, and each step adds one major concept while preserving as much of the previous example structure as possible.
Across the progression examples, the same basic problem is retained so the reader can focus on what changes in the software structure rather than on a changing mathematical model. The examples also print the evolving solution in a simple table with columns for the step index, time, 
The tutorial sequence introduces the following concepts:
Basic Problem - baseline application code for the van der Pol problem using raw C++ arrays and a hand-written Forward Euler loop.
Utilize Thyra - replace raw arrays with Thyra vectors and vector-space abstractions.
Use ModelEvaluator - use Thyra::ModelEvaluator to describe the problem model.
Introduce SolutionState - introduce Tempus::SolutionState to store the solution and selected integration metadata.
Add SolutionHistory - introduce Tempus::SolutionHistory to manage current and working solution states during time integration.
Introduce Stepper - introduce Tempus::Stepper through Tempus::StepperForwardEuler to perform Forward Euler timesteps.
Introduce TimeStepControl - introduce Tempus::TimeStepControl to control timestep sizes independently of the stepper.
Utilize IntegratorBasic - use Tempus::IntegratorBasic to manage the overall time integration process.
This progression is intended to show how applications can adopt Tempus incrementally rather than all at once.
How to read these examples
A recommended reading order is:
- read the current example source
- read the transition page describing what changed from the previous step
- compare the files directly when line-by-line detail is needed
The early examples show the control flow explicitly in application code. Later examples move more of that responsibility into Tempus objects such as Tempus::SolutionState, Tempus::SolutionHistory, Tempus::Stepper, and Tempus::TimeStepControl. This progression is intentional: the tutorials are designed to make it clear which pieces of logic remain in the application and which pieces are delegated to Tempus as the abstraction level increases.
