1(integrator_table)= 2 3# Summary of Time Integrators Available In PETSc 4 5```{eval-rst} 6.. list-table:: Time integration schemes 7 :name: tab_TSPET 8 :header-rows: 1 9 10 * - TS Name 11 - Reference 12 - Class 13 - Type 14 - Order 15 * - euler 16 - forward Euler 17 - one-step 18 - explicit 19 - :math:`1` 20 * - ssp 21 - multistage SSP :cite:`ketcheson_2008` 22 - Runge-Kutta 23 - explicit 24 - :math:`\le 4` 25 * - rk* 26 - multiscale 27 - Runge-Kutta 28 - explicit 29 - :math:`\ge 1` 30 * - beuler 31 - backward Euler 32 - one-step 33 - implicit 34 - :math:`1` 35 * - cn 36 - Crank-Nicolson 37 - one-step 38 - implicit 39 - :math:`2` 40 * - theta* 41 - theta-method 42 - one-step 43 - implicit 44 - :math:`\le 2` 45 * - bdf 46 - Backward Differentiation Formulas 47 - one-step 48 - implicit 49 - :math:`\le 6` 50 * - alpha 51 - alpha-method :cite:`jansen_2000` 52 - one-step 53 - implicit 54 - :math:`2` 55 * - gl 56 - general linear :cite:`butcher_2007` 57 - multistep-multistage 58 - implicit 59 - :math:`\le 3` 60 * - eimex 61 - extrapolated IMEX :cite:`constantinescu_a2010a` 62 - one-step 63 - IMEX 64 - :math:`\ge 1`, adaptive 65 * - dirk 66 - DIRK 67 - diagonally implicit Runge-Kutta 68 - implicit 69 - :math:`\ge 1` 70 * - arkimex 71 - See :any:`tab_IMEX_RK_PETSc` 72 - IMEX Runge-Kutta 73 - IMEX 74 - :math:`1-5` 75 * - rosw 76 - See :any:`tab_IMEX_RosW_PETSc` 77 - Rosenbrock-W 78 - linearly implicit 79 - :math:`1-4` 80 * - glee 81 - See :any:`tab_IMEX_GLEE_PETSc` 82 - GL with global error 83 - explicit and implicit 84 - :math:`1-3` 85 * - mprk 86 - Multirate Partitioned Runge-Kutta 87 - multirate 88 - explicit 89 - :math:`2-3` 90 * - basicsymplectic 91 - Basic symplectic integrator for separable Hamiltonian 92 - semi-implicit Euler and Velocity Verlet 93 - explicit 94 - :math:`1-2` 95 * - irk 96 - fully implicit Runge-Kutta 97 - Gauss-Legrendre 98 - implicit 99 - :math:`2s` 100``` 101 102```{eval-rst} 103.. bibliography:: /petsc.bib 104 :filter: docname in docnames 105``` 106