psanan/tsmultiscale

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250+ commits behind master.  
update to TS tutorial ex35 for TSFHMMHEUN



TSFHMMHEUN with nonadaptive coarse solver
A 'forward only' HMM method which uses Heun's method at the coarse scale.



TS tutorial ex35, stellar toy



TSMULTIFHMMFE with nonadaptive coarse solver
A simple HMM multiscale integrator, as described in Ariel, Engquist, Tsai, Kim, and Lee 2012.



minor edits in rk and adding petsc math types in ex31



Added comments documenting the DormandPrince and BogackiShampine RK methods...



Added a Boolean variable to indicate of method is FSAL



Added DormandPrince and BogackiShampine RK schemes...



Implemented the renovated RK.
The first 6 commits are squashed and the text is preserved below.
modified the comment in rk.c
Copied arkimex.c to rk.c... will now start removing the implicit parts..
Renamed all ARKIMEX to RK in the variables... edited the structures representing the RK scheme...
Rough cut: removed all implicit stuff from ARKIMEX to get RK... have registered forward Euler, RK2 and RK3...
TSRK is *sort of* running... with probably some issues that need to be ironed out...
…



TSMULTI
Adds a new TS package designed for mutiscale integrators
with wellseparated timescales, of the form
du/dt = (1/epsilon) f(u,t) + g(u,t)
which admit a change of variables of the form
dx/dt = (1/epsilon) F(x,y,t) + G(x,y,t)
dy/dt = H(x,y,t)
Where the flow of x exhibits ergodicity with respect to some measure indexed by y, thus
allowing one to conclude that, in the limit as epsilon>infinity, y …



TS Partitioned Righthand Sides
Adds support for multiple RHS functions, RHS function Jacobians, and RHS function user contexts,
referred to with enumerated types TSRHSPartitionType and TSRHSPartitionSlotType.
These partitionings are intended to be used with new TS implementations requiring partitioned
right hand sides, including sympelctic, exponential, and multiscale integrators.

