Generated by scripts/generate_catalog.py from the runtime registry.
142 registered schemes across 11 families, with orders through 14 and 47 estimate emitters.
Stored stages include endpoint rows. A driver without a fixed stage count
shows driver or its per-step stage options; a nonzero null-stage
companion weight adds one RHS call outside the coupled solve. These are stage counts, not total
RHS evaluations or solver work. The estimate exponent q is the value to
pass to propose_dt, and can differ from the propagated order.
An empty required-RHS set permits a combined plain callable. IMEX splits
are optional; KenCarp/ARS DIRKs supply their pure implicit tableaus.
Stability labels and reuse qualifications are explained in the family pages.
Friendly names spell out authors and method constructions. The enum column
gives the exact family member accepted by get_scheme, for example
get_scheme(ExplicitRK.tsit5) for Tsitouras 5(4). Family members share
their values with IntegrationSchemeType. Existing lookup strings keep
their original spelling; these documentation labels do not add string aliases.
Explicit RK — 63 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Forward Euler | ExplicitRK.forwardEuler | 1 | 1 | — | — | — | refused | combined | tensor |
| Explicit midpoint (Runge–Kutta 2) | ExplicitRK.rungeKutta2 | 2 | 2 | — | — | — | 2 | combined | tensor |
| Heun's Method (2nd order) | ExplicitRK.heunsMethod | 2 | 2 | — | — | — | 2 | combined | tensor |
| Ralston's Method (2nd order) | ExplicitRK.ralston2nd | 2 | 2 | — | — | — | 1 | combined | tensor |
| Classical Runge–Kutta 3 | ExplicitRK.rungeKutta3 | 3 | 3 | — | — | — | 2 | combined | tensor |
| Heun's Method (3rd order) | ExplicitRK.heunsMethod3rd | 3 | 3 | — | — | — | 1 | combined | tensor |
| Ralston's Method (3rd order) | ExplicitRK.ralston3rd | 3 | 3 | — | — | — | 1 | combined | tensor |
| Wray's Method (3rd order) | ExplicitRK.wray3rd | 3 | 3 | — | — | — | 1 | combined | tensor |
| Shu–Osher SSP Runge–Kutta 3 | ExplicitRK.sspRK3 | 3 | 3 | — | — | — | 1 | combined | tensor |
| SSP Runge–Kutta (10 stages, order 4) | ExplicitRK.ssprk104 | 4 | 10 | — | — | — | 3 | combined | tensor |
| SSP Runge–Kutta (5 stages, order 3) | ExplicitRK.ssprk53 | 3 | 5 | — | — | — | 1 | combined | tensor |
| SSP Runge–Kutta (6 stages, order 3) | ExplicitRK.ssprk63 | 3 | 6 | — | — | — | 1 | combined | tensor |
| SSP Runge–Kutta (7 stages, order 3) | ExplicitRK.ssprk73 | 3 | 7 | — | — | — | 1 | combined | tensor |
| SSP Runge–Kutta (8 stages, order 3) | ExplicitRK.ssprk83 | 3 | 8 | — | — | — | 1 | combined | tensor |
| SSP Runge–Kutta (5 stages, order 4) | ExplicitRK.ssprk54 | 4 | 5 | — | — | — | 1 | combined | tensor |
| Kubatko–Yeager–Ketcheson SSP RK2 (4 stages) | ExplicitRK.kykssprk42 | 2 | 4 | — | — | — | 1 | combined | tensor |
| Kubatko–Yeager–Ketcheson DG SSP RK2 (3 stages) | ExplicitRK.kyk2014dgssprk3s2 | 2 | 3 | — | — | — | 1 | combined | tensor |
| SSP Runge–Kutta 3(2) (4 stages, comparison 1) | ExplicitRK.ssprk43 | 3 | 4 | 2 | 3 | — | 1 | combined | tensor |
| SSP Runge–Kutta 3(2) (4 stages, comparison 2) | ExplicitRK.ssprk432 | 3 | 4 | 2 | 3 | — | 1 | combined | tensor |
| SSP Runge–Kutta 3 (9 stages) | ExplicitRK.ssprk932 | 3 | 9 | — | — | — | 1 | combined | tensor |
| Higueras–Roldán SSP RK3 (2N1 variant) | ExplicitRK.ssprk53_2n1 | 3 | 5 | — | — | — | 1 | combined | tensor |
| Higueras–Roldán SSP RK3 (2N2 variant) | ExplicitRK.ssprk53_2n2 | 3 | 5 | — | — | — | 1 | combined | tensor |
| Higueras–Roldán SSP RK3 (H variant) | ExplicitRK.ssprk53_h | 3 | 5 | — | — | — | 1 | combined | tensor |
| Classical Runge–Kutta 4 | ExplicitRK.rungeKutta4 | 4 | 4 | — | — | — | 3 | combined | tensor |
| Runge–Kutta 4 (3/8 rule) | ExplicitRK.rungeKutta4alt | 4 | 4 | — | — | — | 2 | combined | tensor |
| Nyström Runge–Kutta 5 | ExplicitRK.nystrom5th | 5 | 6 | — | — | — | 1 | combined | tensor |
| Bogacki–Shampine 3(2) | ExplicitRK.bogackiShampine | 3 | 4 | 2 | 3 | — | 3 (FSAL) | combined | tensor |
| Dormand–Prince 5(4) | ExplicitRK.dormandPrince | 5 | 7 | 4 | 5 | — | 5 (FSAL) | combined | tensor |
| Cash–Karp 5(4) | ExplicitRK.cashKarp | 5 | 6 | 4 | 5 | — | 1 | combined | tensor |
| Tsitouras 5(4) | ExplicitRK.tsit5 | 5 | 7 | 4 | 5 | — | 5 (FSAL) | combined | tensor |
| Owren–Zennaro 3(2) | ExplicitRK.owrenzen3 | 3 | 4 | 2 | 3 | — | 3 (FSAL) | combined | tensor |
| Owren–Zennaro 4(3) | ExplicitRK.owrenzen4 | 4 | 6 | 3 | 4 | — | 4 (FSAL) | combined | tensor |
| Owren–Zennaro 5(4) | ExplicitRK.owrenzen5 | 5 | 8 | 4 | 5 | — | 5 (FSAL) | combined | tensor |
| Bogacki–Shampine 5(4) | ExplicitRK.bs5 | 5 | 8 | 4 | 5 | — | 5 (FSAL) | combined | tensor |
| Stepanov 5(4) (7 stages) | ExplicitRK.stefanov5 | 5 | 7 | 4 | 5 | — | 5 (FSAL) | combined | tensor |
| Alshina–Zaks–Kalitkin 2(1) | ExplicitRK.arushina2 | 2 | 2 | 1 | 2 | — | 1 | combined | tensor |
| Alshina–Zaks–Kalitkin 3 | ExplicitRK.arushina3 | 3 | 3 | — | — | — | 1 | combined | tensor |
| Alshina–Zaks–Kalitkin 6 | ExplicitRK.arushina6 | 6 | 7 | — | — | — | 4 | combined | tensor |
| Stepanov 5 (9 stages) | ExplicitRK.msrk5 | 5 | 9 | — | — | — | 5 (FSAL) | combined | tensor |
| Stepanov 6 (9 stages) | ExplicitRK.msrk6 | 6 | 9 | — | — | — | 6 (FSAL) | combined | tensor |
| Kovalnogov–Simos–Tsitouras 5 (SIR method) | ExplicitRK.sir54 | 5 | 8 | — | — | — | 5 (FSAL) | combined | tensor |
| Ralston Runge–Kutta 4 | ExplicitRK.raston4 | 4 | 4 | — | — | — | 2 | combined | tensor |
| Runge–Kutta–Oliver 5 (6 stages) | ExplicitRK.rko65 | 5 | 6 | — | — | — | 5 | combined | tensor |
| Mead–Renaut Runge–Kutta 3 | ExplicitRK.rkm | 3 | 6 | — | — | — | 1 | combined | tensor |
| Pseudo-symplectic Runge–Kutta 4 (6 stages) | ExplicitRK.psrk4p7q6 | 4 | 6 | — | — | — | 4 | combined | tensor |
| Pseudo-symplectic Runge–Kutta 3 (5 stages) | ExplicitRK.psrk3p6q5 | 3 | 5 | — | — | — | 3 | combined | tensor |
| Pseudo-symplectic Runge–Kutta 3 (4 stages) | ExplicitRK.psrk3p5q4 | 3 | 4 | — | — | — | 3 | combined | tensor |
| Verner 6(5) | ExplicitRK.vern6 | 6 | 9 | 5 | 6 | — | 6 (FSAL) | combined | tensor |
| Verner 7(6) | ExplicitRK.vern7 | 7 | 10 | 6 | 7 | — | refused | combined | tensor |
| Verner 8(7) | ExplicitRK.vern8 | 8 | 13 | 7 | 8 | — | 5 | combined | tensor |
| Verner 9(8) | ExplicitRK.vern9 | 9 | 16 | 8 | 9 | — | 6 | combined | tensor |
| Verner 7(6) (RKV76.IIa) | ExplicitRK.rkv76iia | 7 | 10 | 6 | 7 | — | refused | combined | tensor |
| Tanaka–Muramatsu–Yamashita 7(6) | ExplicitRK.tanyam7 | 7 | 10 | 6 | 7 | — | refused | combined | tensor |
| Tsitouras–Papakostas 8(7) | ExplicitRK.tsitpap8 | 8 | 13 | 7 | 8 | — | 5 | combined | tensor |
| Dormand–Prince 8 | ExplicitRK.dp8 | 8 | 12 | — | — | — | 5 | combined | tensor |
| Feagin Runge–Kutta 10 | ExplicitRK.feagin10 | 10 | 17 | — | — | — | 6 | combined | tensor |
| Feagin Runge–Kutta 12 | ExplicitRK.feagin12 | 12 | 25 | — | — | — | 6 | combined | tensor |
| Feagin Runge–Kutta 14 | ExplicitRK.feagin14 | 14 | 35 | — | — | — | refused | combined | tensor |
| Evaluate–predict–evaluate–correct (midpoint) | ExplicitRK.epec | 2 | 2 | — | — | — | 2 | combined | tensor |
| Evaluate–predict–evaluate–correct (Heun) | ExplicitRK.epecModified | 2 | 2 | — | — | — | 2 | combined | tensor |
| TVD Runge–Kutta 3 (Shu–Osher) | ExplicitRK.tvdRK3 | 3 | 3 | — | — | — | refused | combined | tensor |
| TVD Runge–Kutta 2 (Shu–Osher) | ExplicitRK.tvdRK2 | 2 | 2 | — | — | — | refused | combined | tensor |
| Explicit Euler | ExplicitRK.explicitEuler | 1 | 1 | — | — | — | refused | combined | tensor |
Symplectic — 6 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Leapfrog (synchronized) | Symplectic.leapFrog | 2 | driver | — | — | — | 1 | combined | position/velocity; separability assumptions |
| Symplectic Euler | Symplectic.symplecticEuler | 2 | driver | — | — | — | 1 | combined | position/velocity; separability assumptions |
| Velocity Verlet | Symplectic.velocityVerlet | 2 | driver | — | — | — | 2 | combined | position/velocity; separability assumptions |
| Forest–Ruth 4 (position-first, PEFRL) | Symplectic.pefrl | 4 | driver | — | — | — | refused | combined | position/velocity; separability assumptions |
| Forest–Ruth 4 (velocity-first, VEFRL) | Symplectic.vefrl | 4 | driver | — | — | — | refused | combined | position/velocity; separability assumptions |
| Semi-Implicit Euler | Symplectic.semiImplicitEuler | 1 | 1 | — | — | — | refused | combined | position/velocity |
Relaxed Chebyshev — 3 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Runge–Kutta–Chebyshev 1 | RelaxedChebyshev.rkc1 | 1 | variable | — | — | — | refused | combined; lambda_max= or s= | tensor |
| Runge–Kutta–Chebyshev 2 | RelaxedChebyshev.rkc2 | 2 | variable | — | — | — | refused | combined; lambda_max= or s= | tensor |
| Runge–Kutta–Legendre 2 | RelaxedChebyshev.rkl2 | 2 | variable | — | — | — | refused | combined; lambda_max= or s= | tensor |
Multistep explicit — 10 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Adams-Bashforth 2 | MultistepExplicit.ab2 | 2 | driver | — | — | — | refused | combined | tensor; 1 previous entries |
| Adams-Bashforth 3 | MultistepExplicit.ab3 | 3 | driver | — | — | — | refused | combined | tensor; 2 previous entries |
| Adams-Bashforth 4 | MultistepExplicit.ab4 | 4 | driver | — | — | — | refused | combined | tensor; 3 previous entries |
| Adams-Bashforth 5 | MultistepExplicit.ab5 | 5 | driver | — | — | — | refused | combined | tensor; 4 previous entries |
| Adams-Bashforth-Moulton 2 (PECE) | MultistepExplicit.abm2 | 2 | driver | — | — | — | refused | combined | tensor; 1 previous entries |
| Adams-Bashforth-Moulton 3 (PECE) | MultistepExplicit.abm3 | 3 | driver | — | — | — | refused | combined | tensor; 2 previous entries |
| Adams-Bashforth-Moulton 4 (PECE) | MultistepExplicit.abm4 | 4 | driver | — | — | — | refused | combined | tensor; 3 previous entries |
| Adams-Bashforth-Moulton 5 (PECE) | MultistepExplicit.abm5 | 5 | driver | — | — | — | refused | combined | tensor; 4 previous entries |
| SSP multistep (3 steps, order 2) | MultistepExplicit.ssprkmsvs32 | 2 | driver | — | — | — | refused | combined | tensor; 2 previous entries |
| SSP multistep (4 steps, order 3) | MultistepExplicit.ssprkmsvs43 | 3 | driver | — | — | — | refused | combined | tensor; 3 previous entries |
DIRK — 37 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Backward Euler (implicit) | DIRK.backwardEuler | 1 | 1 | — | — | L | refused | combined | tensor |
| Implicit Midpoint | DIRK.implicitMidpoint | 2 | 1 | — | — | A | refused | combined | tensor |
| Trapezoidal (Crank-Nicolson) | DIRK.trapezoidal | 2 | 2 | — | — | A | 2 (FSAL) | combined | tensor |
| Singly diagonally implicit Runge–Kutta 2 | DIRK.sdirk2 | 2 | 2 | — | — | L | refused | combined | tensor |
| Trapezoidal rule–BDF2 (TR-BDF2) | DIRK.trbdf2 | 2 | 3 | 3 | 3 | L | 2 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 3(2) (4 stages) | DIRK.esdirk324l2sa | 3 | 4 | 2 | 3 | L | 3 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 4(3) (6 stages) | DIRK.esdirk436l2sa | 4 | 6 | 3 | 4 | L | 4 (FSAL) | combined | tensor |
| Kværnø 3(2) | DIRK.kvaerno3 | 3 | 4 | 2 | 3 | L | 3 (FSAL) | combined | tensor |
| Kværnø 4(3) | DIRK.kvaerno4 | 4 | 5 | 3 | 4 | A | 4 (FSAL) | combined | tensor |
| Kværnø 5(4) | DIRK.kvaerno5 | 5 | 7 | 4 | 5 | L | 5 (FSAL) | combined | tensor |
| Kennedy–Carpenter 3(2) (4 stages, KenCarp3) | DIRK.kencarp3 | 3 | 4 | 2 | 3 | L | 3 (FSAL) | combined | tensor |
| Kennedy–Carpenter 4(3) (6 stages, KenCarp4) | DIRK.kencarp4 | 4 | 6 | 3 | 4 | L | 4 (FSAL) | combined | tensor |
| Kennedy–Carpenter 4(3) (7 stages, KenCarp47) | DIRK.kencarp47 | 4 | 7 | 3 | 4 | L | 4 (FSAL) | combined | tensor |
| Kennedy–Carpenter 5(4) (8 stages, KenCarp5) | DIRK.kencarp5 | 5 | 8 | 4 | 5 | L | 5 (FSAL) | combined | tensor |
| Kennedy–Carpenter 5(4) (8 stages, KenCarp58) | DIRK.kencarp58 | 5 | 8 | 4 | 5 | L | 5 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 3(2) (5 stages) | DIRK.esdirk325l2sa | 3 | 5 | 2 | 3 | L | 3 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 4(3) (6 stages, variant 2) | DIRK.esdirk436l2sa2 | 4 | 6 | 3 | 4 | L | 4 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 4(3) (7 stages) | DIRK.esdirk437l2sa | 4 | 7 | 3 | 4 | L | 4 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 5(4) (7 stages, variant 2) | DIRK.esdirk547l2sa2 | 5 | 7 | 4 | 5 | L | 5 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 5(4) (8 stages, I variant) | DIRK.esdirk54i8l2sa | 5 | 8 | 4 | 5 | L | 5 (FSAL) | combined | tensor |
| Explicit-first-stage SDIRK 6(5) (9 stages) | DIRK.esdirk659l2sa | 6 | 9 | 5 | 6 | L | 6 (FSAL) | combined | tensor |
| SSP singly diagonally implicit Runge–Kutta 2 | DIRK.sspsdirk2 | 2 | 2 | — | — | A | refused | combined | tensor |
| Ascher–Ruuth–Spiteri (ARS222, implicit part) | DIRK.ars222 | 2 | 3 | — | — | L | 2 (FSAL) | combined | tensor |
| Ascher–Ruuth–Spiteri (ARS232, implicit part) | DIRK.ars232 | 2 | 3 | — | — | L | 2 (FSAL) | combined | tensor |
| Ascher–Ruuth–Spiteri (ARS343, implicit part) | DIRK.ars343 | 3 | 4 | — | — | L | 3 (FSAL) | combined | tensor |
| Ascher–Ruuth–Spiteri (ARS443, implicit part) | DIRK.ars443 | 3 | 5 | — | — | L | 3 (FSAL) | combined | tensor |
| Boscarino–Russo 3 (BHR553, implicit part) | DIRK.bhr553 | 3 | 5 | — | — | L | 3 (FSAL) | combined | tensor |
| Cash SDIRK 4(3) | DIRK.cash4 | 4 | 5 | 3 | 4 | L | refused | combined | tensor |
| Calvo–de Frutos–Novo 3 (implicit part) | DIRK.cfnlirk3 | 3 | 4 | — | — | L | 3 (FSAL) | combined | tensor |
| Hairer–Wanner SDIRK 4(3) (variant 1) | DIRK.hairer4 | 4 | 5 | 3 | 4 | L | refused | combined | tensor |
| Hairer–Wanner SDIRK 4(3) (variant 2) | DIRK.hairer42 | 4 | 5 | 3 | 4 | L | refused | combined | tensor |
| Ferracina–Spijker SDIRK 4 (4 stages) | DIRK.sfstdirk4 | 4 | 4 | — | — | — | refused | combined | tensor |
| Ferracina–Spijker SDIRK 4 (5 stages) | DIRK.sfstdirk5 | 4 | 5 | — | — | — | refused | combined | tensor |
| Ferracina–Spijker SDIRK 4 (6 stages) | DIRK.sfstdirk6 | 4 | 6 | — | — | — | refused | combined | tensor |
| Ferracina–Spijker SDIRK 4 (7 stages) | DIRK.sfstdirk7 | 4 | 7 | — | — | — | refused | combined | tensor |
| Ferracina–Spijker SDIRK 4 (8 stages) | DIRK.sfstdirk8 | 4 | 8 | — | — | — | refused | combined | tensor |
| Modified extended backward differentiation 2 | DIRK.mebdf2 | 2 | 3 | — | — | L | refused | combined | tensor |
Coupled RK — 4 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Gauss–Legendre collocation (2 stages) | CoupledRK.gaussLegendre2 | 4 | 2 + 1 companion | 2 | 3 | A | refused | combined | tensor |
| Radau IIA collocation (2 stages) | CoupledRK.radauIia2 | 3 | 2 + 1 companion | 2 | 3 | L | refused | combined | tensor |
| Gauss–Legendre collocation (3 stages) | CoupledRK.gaussLegendre3 | 6 | 3 | 2 | 3 | A | refused | combined | tensor |
| Radau IIA collocation (3 stages) | CoupledRK.radauIia3 | 5 | 3 + 1 companion | 3 | 4 | L | refused | combined | tensor |
Multistep implicit — 8 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Backward differentiation formula 1 | MultistepImplicit.bdf1 | 1 | driver | — | — | L | refused | combined | tensor; 1 previous entries |
| Backward differentiation formula 2 | MultistepImplicit.bdf2 | 2 | driver | — | — | A | refused | combined | tensor; 1 previous entries |
| Backward differentiation formula 3 | MultistepImplicit.bdf3 | 3 | driver | — | — | A(alpha) | refused | combined | tensor; 2 previous entries |
| Backward differentiation formula 4 | MultistepImplicit.bdf4 | 4 | driver | — | — | A(alpha) | refused | combined | tensor; 3 previous entries |
| Backward differentiation formula 5 | MultistepImplicit.bdf5 | 5 | driver | — | — | A(alpha) | refused | combined | tensor; 4 previous entries |
| Adams-Moulton 2 (implicit) | MultistepImplicit.am2 | 2 | driver | — | — | A | refused | combined | tensor; 1 previous entries |
| Adams-Moulton 3 (implicit) | MultistepImplicit.am3 | 3 | driver | — | — | — | refused | combined | tensor; 2 previous entries |
| Adams-Moulton 4 (implicit) | MultistepImplicit.am4 | 4 | driver | — | — | — | refused | combined | tensor; 3 previous entries |
IMEX — 7 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Kennedy–Carpenter additive RK 3(2) (4 stages) | IMEX.ark324l2sa | 3 | 4 | 2 | 3 | L | refused | combined | tensor |
| Kennedy–Carpenter additive RK 4(3) (6 stages) | IMEX.ark436l2sa | 4 | 6 | 3 | 4 | L | refused | combined | tensor |
| Implicit–explicit Euler | IMEX.imexEuler | 1 | driver | — | — | A | refused | combined | tensor |
| Semi-implicit backward differentiation 2 | IMEX.sbdf2 | 2 | driver | — | — | L | refused | combined | tensor; 1 previous entries |
| Semi-implicit backward differentiation 3 | IMEX.sbdf3 | 3 | driver | — | — | A(alpha) | refused | combined | tensor; 2 previous entries |
| Crank–Nicolson–Adams–Bashforth 2 | IMEX.cnab2 | 2 | driver | — | — | A | refused | combined | tensor; 1 previous entries |
| Crank–Nicolson–leapfrog 2 | IMEX.cnlf2 | 2 | driver | — | — | A | refused | combined | tensor; 1 previous entries |
Linearly implicit — 1 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Rosenbrock–W 3(2) (ROS3P) | LinearlyImplicit.ros3p | 3 | 3 | 2 | 3 | A | refused | combined | tensor |
Exponential — 2 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Exponential time-differencing Runge–Kutta 2 | Exponential.etd2rk | 2 | 2 | — | — | L | refused | linear | tensor |
| Exponential Rosenbrock 3(2) | Exponential.exprb32 | 3 | 2 | 2 | 3 | L | refused | combined | tensor |
Newmark — 1 schemes
Equations and qualifications.
| Friendly name | Enum member | Order | Stages | Companion order | Estimate q | Stability | Reuse order | Required RHS / options | State / history |
|---|
| Newmark (average acceleration by default) | Newmark.newmark | 2 | driver | — | — | A | refused | combined | position/velocity |