ODE Tableaus
Explicit Runge-Kutta Methods
constructEuler
- Euler's 1st order method.constructHeun()
Heun'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 LobattoIIIAconstructLobattoIIIB2
- The 2nd order LobattoIIIBconstructLobattoIIIB4
- The 4th order LobattoIIIBconstructLobattoIIIC2
- The 2nd order LobattoIIICconstructLobattoIIIC4
- The 4th order LobattoIIICconstructLobattoIIICStar2
- The 2nd order LobattoIIIC*constructLobattoIIICStar4
- The 4th order LobattoIIIC*constructLobattoIIID2
- The 2nd order LobattoIIIDconstructLobattoIIID4
- The 4th order LobattoIIIDconstructRadauIA3
- The 3rd order RadauIAconstructRadauIA5
- The 5th order RadauIAconstructRadauIIA3
- The 3rd order RadauIIAconstructRadauIIA5
- The 5th order RadauIIA
Tableau Methods
DiffEqDevTools.stability_region
— Functionstability_region(z,tab::ODERKTableau)
Calculates the stability function from the tableau at z
. Stable if <1.
\[r(z) = 1 + z bᵀ(I - zA)⁻¹ e\]
where e denotes a vector of ones.
stability_region(tab::ODERKTableau; initial_guess=-3.0)
Calculates the length of the stability region in the real axis.
OrdinaryDiffEq.ODE_DEFAULT_TABLEAU
— ConstantODEDEFAULTTABLEAU
Sets the default tableau for the ODE solver. Currently Dormand-Prince 4/5.
Explicit Tableaus
DiffEqDevTools.constructEuler
— FunctionEuler's method.
DiffEqDevTools.constructRalston
— FunctionRalston's Order 2 method.
DiffEqDevTools.constructHeun
— FunctionHeun's Order 2 method.
DiffEqDevTools.constructKutta3
— FunctionKutta's Order 3 method.
Missing docstring for OrdinaryDiffEq.constructBS3
. Check Documenter's build log for details.
DiffEqDevTools.constructBogakiShampine3
— FunctionconstructBogakiShampine3()
Constructs the tableau object for the Bogakai-Shampine Order 2/3 method.
DiffEqDevTools.constructRK4
— FunctionClassic RK4 method.
DiffEqDevTools.constructRK438Rule
— FunctionClassic RK4 3/8's rule method.
DiffEqDevTools.constructRKF4
— FunctionRunge-Kutta-Fehberg Order 4/3
DiffEqDevTools.constructRKF5
— FunctionRunge-Kutta-Fehlberg Order 4/5 method.
DiffEqDevTools.constructCashKarp
— FunctionconstructCashKarp()
Constructs the tableau object for the Cash-Karp Order 4/5 method.
Missing docstring for DiffEqDevTools.constructDormandPrince
. Check Documenter's build log for details.
Missing docstring for OrdinaryDiffEq.constructBS5
. Check Documenter's build log for details.
DiffEqDevTools.constructPapakostasPapaGeorgiou5
— FunctionS.N. Papakostas and G. PapaGeorgiou higher error more stable
A Family of Fifth-order Runge-Kutta Pairs, by S.N. Papakostas and G. PapaGeorgiou, Mathematics of Computation,Volume 65, Number 215, July 1996, Pages 1165-1181.
DiffEqDevTools.constructPapakostasPapaGeorgiou52
— FunctionS.N. Papakostas and G. PapaGeorgiou less stable lower error Strictly better than DP5
A Family of Fifth-order Runge-Kutta Pairs, by S.N. Papakostas and G. PapaGeorgiou, Mathematics of Computation,Volume 65, Number 215, July 1996, Pages 1165-1181.
DiffEqDevTools.constructTsitouras5
— FunctionRunge–Kutta pairs of orders 5(4) using the minimal set of simplifying assumptions, by Ch. Tsitouras, TEI of Chalkis, Dept. of Applied Sciences, GR34400, Psahna, Greece.
DiffEqDevTools.constructLutherKonen5
— FunctionLuther and Konen's First Order 5 Some Fifth-Order Classical Runge Kutta Formulas, H.A.Luther and H.P.Konen, Siam Review, Vol. 3, No. 7, (Oct., 1965) pages 551-558.
DiffEqDevTools.constructLutherKonen52
— FunctionLuther and Konen's Second Order 5 Some Fifth-Order Classical Runge Kutta Formulas, H.A.Luther and H.P.Konen, Siam Review, Vol. 3, No. 7, (Oct., 1965) pages 551-558.
DiffEqDevTools.constructLutherKonen53
— FunctionLuther and Konen's Third Order 5 Some Fifth-Order Classical Runge Kutta Formulas, H.A.Luther and H.P.Konen, Siam Review, Vol. 3, No. 7, (Oct., 1965) pages 551-558.
DiffEqDevTools.constructRungeFirst5
— FunctionRunge's First Order 5 method
DiffEqDevTools.constructLawson5
— FunctionLawson's 5th order scheme
An Order Five Runge Kutta Process with Extended Region of Stability, J. Douglas Lawson, Siam Journal on Numerical Analysis, Vol. 3, No. 4, (Dec., 1966) pages 593-597
DiffEqDevTools.constructSharpSmart5
— FunctionExplicit Runge-Kutta Pairs with One More Derivative Evaluation than the Minimum, by P.W.Sharp and E.Smart, Siam Journal of Scientific Computing, Vol. 14, No. 2, pages. 338-348, March 1993.
DiffEqDevTools.constructBogakiShampine5
— FunctionAn Efficient Runge-Kutta (4,5) Pair by P.Bogacki and L.F.Shampine Computers and Mathematics with Applications, Vol. 32, No. 6, 1996, pages 15 to 28
DiffEqDevTools.constructCassity5
— FunctionCassity's Order 5 method
DiffEqDevTools.constructButcher6
— FunctionButcher's First Order 6 method
On Runge-Kutta Processes of High Order, by J. C. Butcher, Journal of the Australian Mathematical Society, Vol. 4, (1964), pages 179 to 194
DiffEqDevTools.constructButcher62
— FunctionButcher's Second Order 6 method
On Runge-Kutta Processes of High Order, by J. C. Butcher, Journal of the Australian Mathematical Society, Vol. 4, (1964), pages 179 to 194
DiffEqDevTools.constructButcher63
— FunctionButcher's Third Order 6
On Runge-Kutta Processes of High Order, by J. C. Butcher, Journal of the Australian Mathematical Society, Vol. 4, (1964), pages 179 to 194
DiffEqDevTools.constructVernerRobust6
— FunctionFrom Verner's Website
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6A
— FunctionTanakaKasugaYamashitaYazaki Order 6 A
On the Optimization of Some Eight-stage Sixth-order Explicit Runge-Kutta Method, by M. Tanaka, K. Kasuga, S. Yamashita and H. Yazaki, Journal of the Information Processing Society of Japan, Vol. 34, No. 1 (1993), pages 62 to 74.
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6B
— FunctionconstructTanakaKasugaYamashitaYazaki Order 6 B
On the Optimization of Some Eight-stage Sixth-order Explicit Runge-Kutta Method, by M. Tanaka, K. Kasuga, S. Yamashita and H. Yazaki, Journal of the Information Processing Society of Japan, Vol. 34, No. 1 (1993), pages 62 to 74.
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6C
— FunctionconstructTanakaKasugaYamashitaYazaki Order 6 C
On the Optimization of Some Eight-stage Sixth-order Explicit Runge-Kutta Method, by M. Tanaka, K. Kasuga, S. Yamashita and H. Yazaki, Journal of the Information Processing Society of Japan, Vol. 34, No. 1 (1993), pages 62 to 74.
DiffEqDevTools.constructTanakaKasugaYamashitaYazaki6D
— FunctionconstructTanakaKasugaYamashitaYazaki Order 6 D
On the Optimization of Some Eight-stage Sixth-order Explicit Runge-Kutta Method, by M. Tanaka, K. Kasuga, S. Yamashita and H. Yazaki, Journal of the Information Processing Society of Japan, Vol. 34, No. 1 (1993), pages 62 to 74.
DiffEqDevTools.constructHuta6
— FunctionAnton Hutas First Order 6 method
Une amélioration de la méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premièr ordre, by Anton Huta, Acta Fac. Nat. Univ. Comenian Math., Vol. 1, pages 201-224 (1956).
DiffEqDevTools.constructHuta62
— FunctionAnton Hutas Second Order 6 method
Une amélioration de la méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premièr ordre, by Anton Huta, Acta Fac. Nat. Univ. Comenian Math., Vol. 1, pages 201-224 (1956).
DiffEqDevTools.constructVerner6
— FunctionVerner Order 5/6 method
A Contrast of a New RK56 pair with DP56, by Jim Verner, Department of Mathematics. Simon Fraser University, Burnaby, Canada, 2006.
DiffEqDevTools.constructDormandPrince6
— FunctionDormand-Prince Order 5//6 method
P.J. Prince and J. R. Dormand, High order embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics . 7 (1981), pp. 67-75.
DiffEqDevTools.constructSharpVerner6
— FunctionSharp-Verner Order 5/6 method
Completely Imbedded Runge-Kutta Pairs, by P. W. Sharp and J. H. Verner, SIAM Journal on Numerical Analysis, Vol. 31, No. 4. (Aug., 1994), pages. 1169 to 1190.
Missing docstring for DiffEqDevTools.constructVern6
. Check Documenter's build log for details.
DiffEqDevTools.constructClassicVerner6
— FunctionEXPLICIT RUNGE-KUTTA METHODS WITH ESTIMATES OF THE LOCAL TRUNCATION ERROR
DiffEqDevTools.constructChummund6
— FunctionChummund's First Order 6 method
A three-dimensional family of seven-step Runge-Kutta methods of order 6, by G. M. Chammud (Hammud), Numerical Methods and programming, 2001, Vol.2, 2001, pages 159-166 (Advanced Computing Scientific journal published by the Research Computing Center of the Lomonosov Moscow State Univeristy)
DiffEqDevTools.constructChummund62
— FunctionChummund's Second Order 6 method
A three-dimensional family of seven-step Runge-Kutta methods of order 6, by G. M. Chammud (Hammud), Numerical Methods and programming, 2001, Vol.2, 2001, pages 159-166 (Advanced Computing Scientific journal published by the Research Computing Center of the Lomonosov Moscow State Univeristy)
DiffEqDevTools.constructPapakostas6
— FunctionPapakostas's Order 6
On Phase-Fitted modified Runge-Kutta Pairs of order 6(5), by Ch. Tsitouras and I. Th. Famelis, International Conference of Numerical Analysis and Applied Mathematics, Crete, (2006)
DiffEqDevTools.constructLawson6
— FunctionLawson's Order 6
An Order 6 Runge-Kutta Process with an Extended Region of Stability, by J. D. Lawson, Siam Journal on Numerical Analysis, Vol. 4, No. 4 (Dec. 1967) pages 620-625.
DiffEqDevTools.constructTsitourasPapakostas6
— FunctionTsitouras-Papakostas's Order 6
Cheap Error Estimation for Runge-Kutta methods, by Ch. Tsitouras and S.N. Papakostas, Siam Journal on Scientific Computing, Vol. 20, Issue 6, Nov 1999.
DiffEqDevTools.constructDormandLockyerMcCorriganPrince6
— FunctionDormandLockyerMcCorriganPrince Order 6 Global Error Estimation
Global Error estimation with Runge-Kutta triples, by J.R.Dormand, M.A.Lockyer, N.E.McCorrigan and P.J.Prince, Computers and Mathematics with Applications, 18 (1989) pages 835-846.
DiffEqDevTools.constructVernerEfficient6
— FunctionFrom Verner's Website
DiffEqDevTools.constructMikkawyEisa
— FunctionMikkawy-Eisa Order 6
A general four-parameter non-FSAL embedded Runge–Kutta algorithm of orders 6 and 4 in seven stages, by M.E.A. El-Mikkawy and M.M.M. Eisa, Applied Mathematics and Computation, Vol. 143, No. 2, (2003) pages 259 to 267.
DiffEqDevTools.constructVernerEfficient7
— FunctionFrom Verner's website
DiffEqDevTools.constructClassicVerner7
— FunctionEXPLICIT RUNGE-KUTTA METHODS WITH ESTIMATES OF THE LOCAL TRUNCATION ERROR
DiffEqDevTools.constructSharpVerner7
— FunctionCompletely Imbedded Runge-Kutta Pairs, by P.W.Sharp and J.H.Verner, Siam Journal on Numerical Analysis, Vol.31, No.4. (August 1994) pages 1169-1190.
DiffEqDevTools.constructTanakaYamashitaStable7
— FunctionOn the Optimization of Some Nine-Stage Seventh-order Runge-Kutta Method, by M. Tanaka, S. Muramatsu and S. Yamashita, Information Processing Society of Japan, Vol. 33, No. 12 (1992) pages 1512-1526.
DiffEqDevTools.constructSharpSmart7
— FunctionExplicit Runge-Kutta Pairs with One More Derivative Evaluation than the Minimum, by P.W.Sharp and E.Smart, Siam Journal of Scientific Computing, Vol. 14, No. 2, pages. 338-348, March 1993.
DiffEqDevTools.constructTanakaYamashitaEfficient7
— FunctionOn the Optimization of Some Nine-Stage Seventh-order Runge-Kutta Method, by M. Tanaka, S. Muramatsu and S. Yamashita, Information Processing Society of Japan, Vol. 33, No. 12 (1992) pages 1512-1526.
DiffEqDevTools.constructVernerRobust7
— FunctionFrom Verner's website
Missing docstring for OrdinaryDiffEq.constructTanYam7
. Check Documenter's build log for details.
DiffEqDevTools.constructEnrightVerner7
— FunctionThe Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge-Kutta Formulas W. H. Enright SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1419-1445.
DiffEqDevTools.constructDormandPrince8
— FunctionconstructDormandPrice8()
Constructs the tableau object for the Dormand-Prince Order 6/8 method.
DiffEqDevTools.constructRKF8
— FunctionconstructRKF8()
Constructs the tableau object for the Runge-Kutta-Fehlberg Order 7/8 method.
DiffEqDevTools.constructCooperVerner8
— FunctionSome Explicit Runge-Kutta Methods of High Order, by G. J. Cooper and J. H. Verner, SIAM Journal on Numerical Analysis, Vol. 9, No. 3, (September 1972), pages 389 to 405
DiffEqDevTools.constructCooperVerner82
— FunctionSome Explicit Runge-Kutta Methods of High Order, by G. J. Cooper and J. H. Verner, SIAM Journal on Numerical Analysis, Vol. 9, No. 3, (September 1972), pages 389 to 405
DiffEqDevTools.constructTsitourasPapakostas8
— FunctionCheap Error Estimation for Runge-Kutta methods, by Ch. Tsitouras and S.N. Papakostas, Siam Journal on Scientific Computing, Vol. 20, Issue 6, Nov 1999.
DiffEqDevTools.constructEnrightVerner8
— FunctionThe Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge-Kutta Formulas W. H. Enright SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1419-1445.
DiffEqDevTools.constructdverk78
— FunctionJim Verner's "Maple" (dverk78)
DiffEqDevTools.constructClassicVerner8
— FunctionEXPLICIT RUNGE-KUTTA METHODS WITH ESTIMATES OF THE LOCAL TRUNCATION ERROR
DiffEqDevTools.constructDormandPrince8_64bit
— FunctionconstructDormandPrice8_64bit()
Constructs the tableau object for the Dormand-Prince Order 6/8 method with the approximated coefficients from the paper. This works until below 64-bit precision.
DiffEqDevTools.constructCurtis8
— FunctionAn Eighth Order Runge-Kutta process with Eleven Function Evaluations per Step, by A. R. Curtis, Numerische Mathematik, Vol. 16, No. 3 (1970), pages 268 to 277
Missing docstring for OrdinaryDiffEq.constructTsitPap8
. Check Documenter's build log for details.
DiffEqDevTools.constructSharp9
— FunctionJournal of Applied Mathematics & Decision Sciences, 4(2), 183-192 (2000), "High order explicit Runge-Kutta pairs for ephemerides of the Solar System and the Moon".
DiffEqDevTools.constructTsitouras9
— FunctionOptimized explicit Runge-Kutta pairs of order 9(8), by Ch. Tsitouras, Applied Numerical Mathematics, 38 (2001) 123-134.
DiffEqDevTools.constructTsitouras92
— FunctionOptimized explicit Runge-Kutta pairs of order 9(8), by Ch. Tsitouras, Applied Numerical Mathematics, 38 (2001) 123-134.
DiffEqDevTools.constructVernerEfficient9
— FunctionFrom Verner's Webiste
Missing docstring for OrdinaryDiffEq.constructVern9
. Check Documenter's build log for details.
DiffEqDevTools.constructVerner916
— FunctionVerner 1991 First Order 5/6 method
Some Ruge-Kutta Formula Pairs, by J.H.Verner, SIAM Journal on Numerical Analysis, Vol. 28, No. 2 (April 1991), pages 496 to 511.
DiffEqDevTools.constructVerner9162
— FunctionVerner 1991 Second Order 5/6 method
Some Ruge-Kutta Formula Pairs, by J.H.Verner, SIAM Journal on Numerical Analysis, Vol. 28, No. 2 (April 1991), pages 496 to 511.
DiffEqDevTools.constructVernerRobust9
— FunctionFrom Verner's Webiste
DiffEqDevTools.constructFeagin10
— FunctionFeagin10 in Tableau form
Missing docstring for DiffEqDevTools.constructFeagin10Tableau
. Check Documenter's build log for details.
DiffEqDevTools.constructOno10
— FunctionOno10
DiffEqDevTools.constructCurtis10
— FunctionHigh-order Explicit Runge-Kutta Formulae, Their uses, and Limitations, A.R.Curtis, J. Inst. Maths Applics (1975) 16, 35-55.
DiffEqDevTools.constructHairer10
— FunctionA Runge-Kutta Method of Order 10, E. Hairer, J. Inst. Maths Applics (1978) 21, 47-59.
DiffEqDevTools.constructBaker10
— FunctionTom Baker, University of Teeside. Part of RK-Aid http://www.scm.tees.ac.uk/users/u0000251/research/researcht.htm http://www.scm.tees.ac.uk/users/u0000251/j.r.dormand/t.baker/rk10921m/rk10921m
DiffEqDevTools.constructFeagin12
— FunctionTableau form of Feagin12
DiffEqDevTools.constructOno12
— FunctionOn the 25 stage 12th order explicit Runge-Kutta method, by Hiroshi Ono. Transactions of the Japan Society for Industrial and applied Mathematics, Vol. 6, No. 3, (2006) pages 177 to 186
Missing docstring for DiffEqDevTools.constructFeagin12Tableau
. Check Documenter's build log for details.
DiffEqDevTools.constructFeagin14
— FunctionTableau form of Feagin14
Missing docstring for DiffEqDevTools.constructFeagin14Tableau
. Check Documenter's build log for details.
Implicit Tableaus
DiffEqDevTools.constructImplicitEuler
— FunctionImplicit Euler Method
DiffEqDevTools.constructMidpointRule
— FunctionOrder 2 Midpoint Method
DiffEqDevTools.constructTrapezoidalRule
— FunctionOrder 2 Trapezoidal Rule (LobattoIIIA2)
DiffEqDevTools.constructLobattoIIIA4
— FunctionLobattoIIIA Order 4 method
DiffEqDevTools.constructLobattoIIIB2
— FunctionLobattoIIIB Order 2 method
DiffEqDevTools.constructLobattoIIIB4
— FunctionLobattoIIIB Order 4 method
DiffEqDevTools.constructLobattoIIIC2
— FunctionLobattoIIIC Order 2 method
DiffEqDevTools.constructLobattoIIIC4
— FunctionLobattoIIIC Order 4 method
DiffEqDevTools.constructLobattoIIICStar2
— FunctionLobattoIIIC* Order 2 method
DiffEqDevTools.constructLobattoIIICStar4
— FunctionLobattoIIIC* Order 4 method
DiffEqDevTools.constructLobattoIIID2
— FunctionLobattoIIID Order 2 method
DiffEqDevTools.constructLobattoIIID4
— FunctionLobattoIIID Order 4 method
DiffEqDevTools.constructGL2
— FunctionGauss-Legendre Order 2.
DiffEqDevTools.constructGL4
— FunctionGauss-Legendre Order 4.
DiffEqDevTools.constructGL6
— FunctionGauss-Legendre Order 6.
DiffEqDevTools.constructRadauIA3
— FunctionRadauIA Order 3 method
DiffEqDevTools.constructRadauIA5
— FunctionRadauIA Order 5 method
DiffEqDevTools.constructRadauIIA3
— FunctionRadauIIA Order 3 method
DiffEqDevTools.constructRadauIIA5
— FunctionRadauIIA Order 5 method