Algorithms#
The ponio library provides multiple algorithms to solve ODE which must be specify in ponio::solve() or ponio::make_solver_range() functions.
See also
For the explaination of different methods, you can read the time integrators desciption.
List of algorithms
- List of explicit Runge-Kutta methods
euler_texplicit_euler_sub4_trk56_trk56a_trk6es_trk_118_trk_21_trk_22_midpoint_trk_22_ralston_trk_32_best_trk_33_trk_33_233e_trk_33_bogackishampine_trk_33_heun_trk_33_ralston_trk_33_van_der_houwen_trk_44_trk_44_235j_trk_44_38_trk_44_ralston_trk_65_trk_65_236a_trk_76_trk_86_trk_nssp_21_trk_nssp_32_trk_nssp_33_trk_nssp_53_trk_spp_43_trk_ssp_22_heun_trk_ssp_32_trk_ssp_33_trk_ssp_42_trk_ssp_53_trk_ssp_54_trkc_202_trkc_51_trkc_52_t- Embedded methods
- List of diagonal implicit Runge-Kutta methods
- List of embedded Runge-Kutta methods
- List of Lawson Runge-Kutta methods
leuler_tlexplicit_euler_sub4_tlrk56_tlrk56a_tlrk6es_tlrk_118_tlrk_21_tlrk_22_midpoint_tlrk_22_ralston_tlrk_32_best_tlrk_33_tlrk_33_233e_tlrk_33_bogackishampine_tlrk_33_heun_tlrk_33_ralston_tlrk_33_van_der_houwen_tlrk_44_tlrk_44_235j_tlrk_44_38_tlrk_44_ralston_tlrk_65_tlrk_65_236a_tlrk_76_tlrk_86_tlrk_nssp_21_tlrk_nssp_32_tlrk_nssp_33_tlrk_nssp_53_tlrk_spp_43_tlrk_ssp_22_heun_tlrk_ssp_32_tlrk_ssp_33_tlrk_ssp_42_tlrk_ssp_53_tlrk_ssp_54_tlrkc_202_tlrkc_51_tlrkc_52_t- Embedded methods
- List of exponential Runge-Kutta methods
- List of additive Runge-Kutta methods
imex_ars111lpum_timex35ldp_timex46ldp1_timex46ldp2_timex46ldp3_timex35lds1_timex35lds2_timexrk23se_timex_rk23ssp_timex_rk33_spi2_timex_rk33_spi4_timex_rk33_lambda_timex_rk36_se_timex_rk36_spi2_timex_rk48_se_timex_rk48_ssp_timex_ssp1111lpm_timex_ssp2222lm_timex_ssp2222pm_timex_ssp2222um_timex_ssp2332lpm1_timex_ssp2332lpm2_timex_ssp2332lpum_timex_ssp2332lspum_timex_ssp2332lum_t- Embedded methods
- List of extended stabilized Runge-Kutta methods
- List of splitting methods
- List of IMEX stabilized methods
Bibliography#
Assyr Abdulle. Fourth order chebyshev methods with recurrence relation. SIAM Journal on Scientific Computing, 23(6):2041–2054, 2002. doi:10.1137/S1064827500379549.
Assyr Abdulle and Alexei A. Medovikov. Second order chebyshev methods based on orthogonal polynomials. Numerische Mathematik, 2001. doi:10.1007/s002110100292.
Assyr Abdulle and Gilles Vilmart. Pirock: a swiss-knife partitioned implicit–explicit orthogonal runge–kutta chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise. Journal of Computational Physics, 242:869–888, 2013. doi:10.1016/j.jcp.2013.02.009.
Stéphane Descombes, Max Duarte, and Marc Massot. Operator splitting methods with error estimator and adaptive time-stepping. Application to the simulation of combustion phenomena. In Roland Glowinski, Stanley Osher, and Wotao Yin, editors, Splitting Methods in Communication, Imaging, Science, and Engineering, pages 1–13. Springer International Publishing, 2015. doi:10.1007/978-3-319-41589-5.
J.R. Dormand and P.J. Prince. A family of embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 6(1):19–26, 1980. doi:10.1016/0771-050X(80)90013-3.
J. Douglas Lawson. Generalized runge-kutta processes for stable systems with large lipschitz constants. SIAM Journal on Numerical Analysis, 4(3):372–380, 1967. doi:10.1137/0704033.
Chad D. Meyer, Dinshaw S. Balsara, and Tariq D. Aslam. A stabilized runge–kutta–legendre method for explicit super-time-stepping of parabolic and mixed equations. Journal of Computational Physics, 257:594–626, 2014. doi:10.1016/j.jcp.2013.08.021.
P.J. Prince and J.R. Dormand. High order embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 7(1):67–75, 1981. doi:10.1016/0771-050X(81)90010-3.