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Tempus: starting step size for ERK method

James Willenbring requested to merge sconde:starting-step-size into develop

Created by: sconde

  • add RK starting step size routine
  • use new starting stepsize routine only when Embedded/adaptive timestepping
  • In ERK stepper, explicit set the time in workingState metadata.
  • update ERK unit test since the refIstep is now lower due to optimal starting step size computed

@trilinos/tempus

Description

Compute an optimal Initial Time Step for ERK. It could also be used for DIRK steppers. Only cost 2 RHS evaluations and a forward euler step.

Motivation and Context

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  • My commit messages mention the appropriate GitHub issue numbers.
  • My code follows the code style of the affected package(s).
  • My change requires a change to the documentation.
  • I have updated the documentation accordingly.
  • I have read the code contribution guidelines for this project.
  • I have added tests to cover my changes.
  • All new and existing tests passed.
  • No new compiler warnings were introduced.
  • These changes break backwards compatibility.

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