TSARKIMEX/TSTHETA: Rename option for initial guess extrapolation

TS: Refactor TSStep() and TSRollBack()

* TSStep() handles the step counter increment, and not TSStep_XXX().
* TSRollBack() handles the step counter decrement.
* Removed ``time_step_prev`` from the T

TS: Refactor TSStep() and TSRollBack()

* TSStep() handles the step counter increment, and not TSStep_XXX().
* TSRollBack() handles the step counter decrement.
* Removed ``time_step_prev`` from the TS structure. New code should use
ts->ptime - ts->ptime_prev to determine the previous time step size.
* Removed unused ``time_step_orig`` from the TS structure.
* Removed unused ``time_step_since_decrease`` from the TS structure.
* Minor update bouncing ball test examples.
* Regenerate some test examples output.

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TSARKIMEX: Various fixes and enhancements

* Eagerly set default type.
* Refactor accept/reject and rollback.
* Fix setup and reset when changing type.
* Change option name
'-ts_arkimex_initial_gue

TSARKIMEX: Various fixes and enhancements

* Eagerly set default type.
* Refactor accept/reject and rollback.
* Fix setup and reset when changing type.
* Change option name
'-ts_arkimex_initial_guess_extrapolate' -> '-ts_arkimex_extrapolate'

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TSROSW: Various fixes and enhancements

* Eagerly set default type.
* Refactor accept/reject and rollback.
* Fix setup and reset when changing type.

TS: Fix TSView() for TSTHETA and TSALPHA to view the TSAdapt context

Merged in dalcinl/fix-ts-declarations (pull request #450)

TS: Fix function declarations and visibility

some uses of PetscTryMethod() actually require that the

object is correct and the function returns an appropriate value.
Change those calls to PetscUseMethod().

TS: Fix function declarations and visibility

* Most of these fixes where spotted by GCC -Wmissing-declarations

Fixes for issues found with clang static analyzer,
mostly set but unused variables

Time: 1 hour

TSTHETA: Remove unnecessary computation of Xdot in the endpoint variant

TSAdapt: Rework implementation

* Simplify handling of TSAdapt in TSALPHA
* Remove broken adaptivity in TSTHETA and use the same backward difference
aproach from TSALPHA
* Update TSEULER to use TSA

TSAdapt: Rework implementation

* Simplify handling of TSAdapt in TSALPHA
* Remove broken adaptivity in TSTHETA and use the same backward difference
aproach from TSALPHA
* Update TSEULER to use TSAdapt (TODO: rejections and adaptivity)
* Update TSSSP to use TSAdapt (TODO: rejections and adaptivity)

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TS: Move calls to TSPreStep() from implementation to interface

* Make the semantics symmetric with TSPostStep()
* Handle rolled back steps appropriately
* If a callback is ever needed to run at the

TS: Move calls to TSPreStep() from implementation to interface

* Make the semantics symmetric with TSPostStep()
* Handle rolled back steps appropriately
* If a callback is ever needed to run at the begining of each TSStep()
(including rolled back steps and step rejections), we can add a new API
to support this particular need (BTW, patches welcome!)

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TSALPHA: Fix comment and whitespace

TSALPHA: Update to use the new API for weighted LTE evaluation

TSALPHA: Update implementation

* Support for event detection.
* Support for time adaptivity based on approximating the local truncation
error using backward difference formulas.
* Use an step-halv

TSALPHA: Update implementation

* Support for event detection.
* Support for time adaptivity based on approximating the local truncation
error using backward difference formulas.
* Use an step-halving approach in the initial step to compute a consistent
initial state as well as approximating the local truncation error.

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More decreasing visibility of symbols from outside libraries
Also fix a few bugs related to having multiple PETSc libraries

labeled a variety of additional internal functions as static
to prevent them from being publically available in the library

Cause TS_EXACTFINALTIME_MATCHSTEP to error for non-adaptive schemes
This also causes non-adapative schemes to not have a TSAdapt object (which they don't use anyway)

Funded-by: IMEX
Time: .2 hours
R

Cause TS_EXACTFINALTIME_MATCHSTEP to error for non-adaptive schemes
This also causes non-adapative schemes to not have a TSAdapt object (which they don't use anyway)

Funded-by: IMEX
Time: .2 hours
Reported-by: Ed Bueler <elbueler@alaska.edu>

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Require users to explicitly call TSSetExactFinalTime() or use the option -ts_exact_final_time
This will make it more likely they understand what the solution of the ODE solver at the
final time is pr

Require users to explicitly call TSSetExactFinalTime() or use the option -ts_exact_final_time
This will make it more likely they understand what the solution of the ODE solver at the
final time is producing and not mistakenly think it is neccessarily the solution exact at the
final time they requested.

Funded-by: IMEX
Time: 2 hours
Thanks-to: Ed Bueler <elbueler@alaska.edu>

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Merge branch 'maint'

Merge branch 'emil/to-maint-fix-ts-reporting-nonembedded' into maint

Merge branch 'emil/to-maint-fix-euler-interpolation' into maint

Merge branch 'maint'

TSRK: add TSRKSetType() fortran interface

Reported-by: Dietzsch Felix <Felix.Dietzsch@vtc.tu-freiberg.de>

ts: add a more complete error message for methods that do not have embedded counterparts and are used with ts_adapt

Reported-by: https://bitbucket.org/petsc/petsc/issues/121/non-embedded-rk-types-gi

ts: add a more complete error message for methods that do not have embedded counterparts and are used with ts_adapt

Reported-by: https://bitbucket.org/petsc/petsc/issues/121/non-embedded-rk-types-give-unhelpful-error

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