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ODE Tableaus

Explicit Runge-Kutta Methods

  • constructEuler - Euler's 1st order method.
  • constructHuen() Huen's order 2 method.
  • constructRalston() - Ralston's order 2 method.
  • constructSSPRK22() - Explicit SSP method of order 2 using 2 stages.
  • constructKutta3 - Kutta's classic 3rd order method.
  • constructSSPRK33() - Explicit SSP method of order 3 using 3 stages.
  • constructSSPRK43() - Explicit SSP method of order 3 using 4 stages.
  • constructRK4 - The classic 4th order "Runge-Kutta" method.
  • constructRK438Rule - The classic 4th order "3/8th's Rule" method.
  • constructSSPRK104() - Explicit SSP method of order 4 using 10 stages.
  • constructBogakiShampine3() - Bogakai-Shampine's 2/3 method.
  • constructRKF4() - Runge-Kutta-Fehlberg 3/4.
  • constructRKF5() - Runge-Kutta-Fehlberg 4/5.
  • constructRungeFirst5() - Runge's first 5th order method.
  • constructCassity5() - Cassity's 5th order method.
  • constructLawson5() - Lawson's 5th order method.
  • constructLutherKonen5 - Luther-Konen's first 5th order method.
  • constructLutherKonen52() - Luther-Konen's second 5th order method.
  • constructLutherKonen53() - Luther-Konen's third 5th order method.
  • constructPapakostasPapaGeorgiou5() - Papakostas and PapaGeorgiou more stable order 5 method.
  • constructPapakostasPapaGeorgiou52() - Papakostas and PapaGeorgiou more efficient order 5 method.
  • constructTsitouras5() - Tsitouras's order 5 method.
  • constructBogakiShampine5() - Bogaki and Shampine's Order 5 method.
  • constructSharpSmart5() - Sharp and Smart's Order 5 method.
  • constructCashKarp() - Cash-Karp method 4/5.
  • constructDormandPrince() - Dormand-Prince 4/5.
  • constructButcher6() - Butcher's first order 6 method.
  • constructButcher62() - Butcher's second order 6 method.
  • constructButcher63() - Butcher's third order 6 method.
  • constructDormandPrince6() - Dormand-Prince's 5/6 method.
  • constructSharpVerner6() Sharp-Verner's 5/6 method.
  • constructVerner916() - Verner's more efficient order 6 method (1991).
  • constructVerner9162() - Verner's second more efficient order 6 method (1991).
  • constructVernerRobust6() - Verner's "most robust" order 6 method.
  • constructVernerEfficient6() - Verner's "most efficient" order 6 method.
  • constructPapakostas6() - Papakostas's order 6 method.
  • constructLawson6() - Lawson's order 6 method.
  • constructTsitourasPapakostas6() - Tsitouras and Papakostas's order 6 method.
  • constructDormandLockyerMcCorriganPrince6() - the Dormand-Lockyer-McCorrigan-Prince order 6 method.
  • constructTanakaKasugaYamashitaYazaki6A() - Tanaka-Kasuga-Yamashita-Yazaki order 6 method A.
  • constructTanakaKasugaYamashitaYazaki6B() - Tanaka-Kasuga-Yamashita-Yazaki order 6 method B.
  • constructTanakaKasugaYamashitaYazaki6C() - Tanaka-Kasuga-Yamashita-Yazaki order 6 method C.
  • constructTanakaKasugaYamashitaYazaki6D() - Tanaka-Kasuga-Yamashita-Yazaki order 6 method D.
  • constructMikkawyEisa() - Mikkawy and Eisa's order 6 method.
  • constructChummund6() - Chummund's first order 6 method.
  • constructChummund62() - Chummund's second order 6 method.
  • constructHuta6() - Huta's first order 6 method.
  • constructHuta62() - Huta's second order 6 method.
  • constructVerner6() - An old order 6 method attributed to Verner.
  • constructDverk() - The classic DVERK algorithm attributed to Verner.
  • constructClassicVerner6() - A classic Verner order 6 algorithm (1978).
  • constructButcher7() - Butcher's order 7 algorithm.
  • constructClassicVerner7()- A classic Verner order 7 algorithm (1978).
  • constructVernerRobust7() - Verner's "most robust" order 7 algorithm.
  • constructTanakaYamashitaStable7() - Tanaka-Yamashita more stable order 7 algorithm.
  • constructTanakaYamashitaEfficient7() - Tanaka-Yamashita more efficient order 7 algorithm.
  • constructSharpSmart7() - Sharp-Smart's order 7 algorithm.
  • constructSharpVerner7() - Sharp-Verner's order 7 algorithm.
  • constructVerner7() - Verner's "most efficient" order 7 algorithm.
  • constructVernerEfficient7() - Verner's "most efficient" order 7 algorithm.
  • constructClassicVerner8() - A classic Verner order 8 algorithm (1978).
  • constructCooperVerner8() - Cooper-Verner's first order 8 algorithm.
  • constructCooperVerner82() - Cooper-Verner's second order 8 algorithm.
  • constructTsitourasPapakostas8() - Tsitouras-Papakostas order 8 algorithm.
  • constructdverk78() - The classic order 8 DVERK algorithm.
  • constructEnrightVerner8() - Enright-Verner order 8 algorithm.
  • constructCurtis8() - Curtis' order 8 algorithm.
  • constructVerner8() - Verner's "most efficient" order 8 algorithm.
  • constructRKF8() - Runge-Kutta-Fehlberg Order 7/8 method.
  • constructDormandPrice8() - Dormand-Prince Order 7/8 method.
  • constructDormandPrince8_64bit() - Dormand-Prince Order 7/8 method. Coefficients are rational approximations good for 64 bits.
  • constructVernerRobust9() - Verner's "most robust" order 9 method.
  • constructVernerEfficient9() - Verner's "most efficient" order 9 method.
  • constructSharp9() - Sharp's order 9 method.
  • constructTsitouras9() - Tsitouras's first order 9 method.
  • constructTsitouras92() - Tsitouras's second order 9 method.
  • constructCurtis10() - Curtis' order 10 method.
  • constructOno10() - Ono's order 10 method.
  • constructFeagin10Tableau() - Feagin's order 10 method.
  • constructCurtis10() - Curtis' order 10 method.
  • constructBaker10() - Baker's order 10 method.
  • constructHairer10() Hairer's order 10 method.
  • constructFeagin12Tableau() - Feagin's order 12 method.
  • constructOno12() - Ono's order 12 method.
  • constructFeagin14Tableau() Feagin's order 14 method.

Implicit Runge-Kutta Methods

  • constructImplicitEuler - The 1st order Implicit Euler method.
  • constructMidpointRule - The 2nd order Midpoint method.
  • constructTrapezoidalRule - The 2nd order Trapezoidal rule (2nd order LobattoIIIA)
  • constructLobattoIIIA4 - The 4th order LobattoIIIA
  • constructLobattoIIIB2 - The 2nd order LobattoIIIB
  • constructLobattoIIIB4 - The 4th order LobattoIIIB
  • constructLobattoIIIC2 - The 2nd order LobattoIIIC
  • constructLobattoIIIC4 - The 4th order LobattoIIIC
  • constructLobattoIIICStar2 - The 2nd order LobattoIIIC*
  • constructLobattoIIICStar4 - The 4th order LobattoIIIC*
  • constructLobattoIIID2 - The 2nd order LobattoIIID
  • constructLobattoIIID4 - The 4th order LobattoIIID
  • constructRadauIA3 - The 3rd order RadauIA
  • constructRadauIA5 - The 5th order RadauIA
  • constructRadauIIA3 - The 3rd order RadauIIA
  • constructRadauIIA5 - The 5th order RadauIIA

Tableau Methods

DiffEqDevTools.stability_region
OrdinaryDiffEq.ODE_DEFAULT_TABLEAU

Explicit Tableaus

DiffEqDevTools.constructEuler
DiffEqDevTools.constructRalston
DiffEqDevTools.constructHeun
DiffEqDevTools.constructKutta3
OrdinaryDiffEq.constructBS3
DiffEqDevTools.constructBogakiShampine3
DiffEqDevTools.constructRK4
DiffEqDevTools.constructRK438Rule
DiffEqDevTools.constructRKF4
DiffEqDevTools.constructRKF5
DiffEqDevTools.constructCashKarp
DiffEqDevTools.constructDormandPrince
OrdinaryDiffEq.constructBS5
DiffEqDevTools.constructPapakostasPapaGeorgiou5
DiffEqDevTools.constructPapakostasPapaGeorgiou52
DiffEqDevTools.constructTsitouras5
DiffEqDevTools.constructLutherKonen5
DiffEqDevTools.constructLutherKonen52
DiffEqDevTools.constructLutherKonen53
DiffEqDevTools.constructRungeFirst5
DiffEqDevTools.constructLawson5
DiffEqDevTools.constructSharpSmart5
DiffEqDevTools.constructBogakiShampine5
DiffEqDevTools.constructCassity5
DiffEqDevTools.constructButcher6
DiffEqDevTools.constructButcher62
DiffEqDevTools.constructButcher63
DiffEqDevTools.constructVernerRobust6
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6A
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6B
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6C
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6D
DiffEqDevTools.constructHuta6
DiffEqDevTools.constructHuta62
DiffEqDevTools.constructVerner6
DiffEqDevTools.constructDormandPrince6
DiffEqDevTools.constructSharpVerner6
DiffEqDevTools.constructVern6
DiffEqDevTools.constructClassicVerner6
DiffEqDevTools.constructChummund6
DiffEqDevTools.constructChummund62
DiffEqDevTools.constructPapakostas6
DiffEqDevTools.constructLawson6
DiffEqDevTools.constructTsitourasPapakostas6
DiffEqDevTools.constructDormandLockyerMcCorriganPrince6
DiffEqDevTools.constructVernerEfficient6
DiffEqDevTools.constructMikkawyEisa
DiffEqDevTools.constructVernerEfficient7
DiffEqDevTools.constructClassicVerner7
DiffEqDevTools.constructSharpVerner7
DiffEqDevTools.constructTanakaYamashitaStable7
DiffEqDevTools.constructSharpSmart7
DiffEqDevTools.constructTanakaYamashitaEfficient7
DiffEqDevTools.constructVernerRobust7
OrdinaryDiffEq.constructTanYam7
DiffEqDevTools.constructEnrightVerner7
DiffEqDevTools.constructDormandPrince8
DiffEqDevTools.constructRKF8
DiffEqDevTools.constructCooperVerner8
DiffEqDevTools.constructCooperVerner82
DiffEqDevTools.constructTsitourasPapakostas8
DiffEqDevTools.constructEnrightVerner8
DiffEqDevTools.constructdverk78
DiffEqDevTools.constructClassicVerner8
DiffEqDevTools.constructDormandPrince8_64bit
DiffEqDevTools.constructCurtis8
OrdinaryDiffEq.constructTsitPap8
DiffEqDevTools.constructSharp9
DiffEqDevTools.constructTsitouras9
DiffEqDevTools.constructTsitouras92
DiffEqDevTools.constructVernerEfficient9
OrdinaryDiffEq.constructVern9
DiffEqDevTools.constructVerner916
DiffEqDevTools.constructVerner9162
DiffEqDevTools.constructVernerRobust9
DiffEqDevTools.constructFeagin10
DiffEqDevTools.constructFeagin10Tableau
DiffEqDevTools.constructOno10
DiffEqDevTools.constructCurtis10
DiffEqDevTools.constructHairer10
DiffEqDevTools.constructBaker10
DiffEqDevTools.constructFeagin12
DiffEqDevTools.constructOno12
DiffEqDevTools.constructFeagin12Tableau
DiffEqDevTools.constructFeagin14
DiffEqDevTools.constructFeagin14Tableau

Implicit Tableaus

DiffEqDevTools.constructImplicitEuler
DiffEqDevTools.constructMidpointRule
DiffEqDevTools.constructTrapezoidalRule
DiffEqDevTools.constructLobattoIIIA4
DiffEqDevTools.constructLobattoIIIB2
DiffEqDevTools.constructLobattoIIIB4
DiffEqDevTools.constructLobattoIIIC2
DiffEqDevTools.constructLobattoIIIC4
DiffEqDevTools.constructLobattoIIICStar2
DiffEqDevTools.constructLobattoIIICStar4
DiffEqDevTools.constructLobattoIIID2
DiffEqDevTools.constructLobattoIIID4
DiffEqDevTools.constructGL2
DiffEqDevTools.constructGL4
DiffEqDevTools.constructGL6
DiffEqDevTools.constructRadauIA3
DiffEqDevTools.constructRadauIA5
DiffEqDevTools.constructRadauIIA3
DiffEqDevTools.constructRadauIIA5