This example replaces the raw C++ arrays from Example 0: Basic Problem with Thyra vectors and vector spaces. The mathematical problem, timestepper, output pattern, and overall time-integration structure remain essentially unchanged. The main purpose is to introduce the abstract vector interfaces used throughout Tempus and other Trilinos packages.

Changes relative to Example 0: Basic Problem:

Teuchos::RCP is used for memory management
state storage moves from raw arrays to Thyra::VectorBase
a Thyra::VectorSpaceBase is introduced to define the state space
vector initialization and element access use Thyra::DetachedVectorView
vector algebra uses Thyra helper routines such as Thyra::V_VpStV, Thyra::norm, and Thyra::V_V

This example shows how the same application logic can be expressed in terms of abstract numerical objects rather than concrete array storage. That abstraction is a prerequisite for later examples that introduce Thyra::ModelEvaluator and Tempus solution-management objects.

As in Example 0: Basic Problem, the example prints the evolving solution in a simple table with columns for the step index, time, , and . The variable passed continues to indicate whether the explicit stepping loop succeeds, while the final tutorial success condition additionally requires that the final solution satisfy the regression check.

Transition notes: See Transition from Example 0 to Example 1 for a detailed explanation of what changed from Example 0: Basic Problem.

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