Speed up ODE solve

[vpuri3]

1. Pass appropriate jac_prototype, preconditioner to OrdinaryDiffEq
2. Experiment with timesteppers. Need IMEX timestepper so we aren't diffusion limited. CVODE_BDF is very fast but randomly segfaults. Tsit5 is very reliable but explicit.
3. use https://diffeq.sciml.ai/dev/basics/integrator/#stepping_controls to take CFL based timesteps

[vpuri3]

ref - https://diffeq.sciml.ai/stable/types/ode_types/#ode_prob for jacobian stuff.

jvp for heat equation is just the diffusion operator. for convection it will be a little more complicated

[vpuri3]

need SciMLOperators, SparseDiffTools integration done to use linsolve argument like
RadauIIA5(autodiff=false,linsolve=IterativeSolversJL_CG())

SciML/SciMLOperators.jl#55

[vpuri3]

# explicit
odealg = Tsit5()
odealg = SSPRK432()
odealg = SSPRK43()

# implicit
odealg = QNDF(autodiff=false)
odealg = RadauIIA5(autodiff=false)

[vpuri3]

need to do OrdinaryDiffEq + SciMLOperators integration to use jvp argument
SciML/SciMLOperators.jl#55

[vpuri3]

https://github.com/vpuri3/PDEInterfaces.jl/blob/0cb7fae9ac7a8604b9ea7791c2e0702403b4ebe6/examples/fourier/heat_forcing.jl#L56-L68