Solvers

• TSRK(subtype), explicit Runge-Kutta
• TSRosW(subtype), linearly implicit Rosenbrock-W
• TSImplicit(subtype; order), backward Euler, Crank-Nicolson, theta and BDF
• TSIRK(nstages), Gauss-Legendre implicit Runge-Kutta of order 2 * nstages
• TSARKIMEX(subtype), additive Runge-Kutta IMEX, for a SplitODEProblem
• TSDAE(subtype), the same implicit methods applied to a DAEProblem
• TSMPRK(slow, subtype), multirate partitioned Runge-Kutta
• TSBasicSymplectic(subtype), symplectic splitting methods for a DynamicalODEProblem or SecondOrderODEProblem
• TSAlpha2(), generalized-alpha for a SecondOrderODEProblem
• TSGeneric(ts_type), a pass-through to any other PETSc TSType by name

Each has a docstring covering its subtypes, whether it adapts and what it requires, so ?TSRosW at the REPL is the reference. One default worth knowing: PETSc's BDF is order 2, so pass TSImplicit("bdf"; order = 5) when comparing against a higher-order method. Every solver takes petsc_options, a vector of command-line style tokens passed to PETSc for that solve, which are parsed after the options this package sets and so take precedence.