Change save_start to take saveat into consideration

[Vaibhavdixit02]

No description provided.

[coveralls]

Coverage increased (+38.4%) to 65.126% when pulling 29aeafc on Vaibhavdixit02:save_start into cf20288 on JuliaDiffEq:master.

[ChrisRackauckas]

Need to check this test to see if it's the desired behavior: https://travis-ci.org/JuliaDiffEq/OrdinaryDiffEq.jl/jobs/403297358#L957-L1037

[codecov]

Codecov Report

Merging #429 into master will decrease coverage by 4.29%.
The diff coverage is n/a.

@@            Coverage Diff            @@
##           master     #429     +/-   ##
=========================================
- Coverage   47.47%   43.17%   -4.3%     
=========================================
  Files          78       78             
  Lines       23707    23682     -25     
=========================================
- Hits        11254    10225   -1029     
- Misses      12453    13457   +1004

Impacted Files	Coverage Δ
src/solve.jl	71.36% <ø> (-15.5%)	⬇️
src/composite_algs.jl	0% <0%> (-100%)	⬇️
src/perform_step/composite_perform_step.jl	4.34% <0%> (-86.96%)	⬇️
src/composite_solution.jl	0% <0%> (-69.57%)	⬇️
src/iterator_interface.jl	0% <0%> (-46.67%)	⬇️
src/caches/sdirk_caches.jl	0% <0%> (-44.55%)	⬇️
src/perform_step/sdirk_perform_step.jl	0% <0%> (-35.06%)	⬇️
src/exponential_utils.jl	65.7% <0%> (-24.36%)	⬇️
src/nlsolve_utils.jl	80.95% <0%> (-19.05%)	⬇️
src/integrators/integrator_utils.jl	56.59% <0%> (-17.45%)	⬇️
... and 22 more

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[ChrisRackauckas]

I realized that this was a bit more intricate than I had at first thought and the best definition would be implementing the one in my head, so I went ahead and did that. We need to get all of the solver packages uniform to this though.

[ChrisRackauckas]

Don't forget the PR to DiffEqBayes to remove the special handling.