Manage coefficients in Shu-Osher form.
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template<class real_type>
struct dg::ShuOsherTableau< real_type >
Manage coefficients in Shu-Osher form.
Currently only explicit tables that are marked with "Shu-Osher-Form" are available in this form
We follow the naming convention of the ARKode library https://sundials.readthedocs.io/en/latest/arkode/Butcher_link.html (They also provide nice stability plots for their methods) as NAME-S-P-Q or NAME-S-Q, where
- NAME is the author or name of the method
- S is the number of stages in the method
- P is the global order of the embedding
- Q is the global order of the method
| Name | Identifier | Description |
| Euler | dg::EXPLICIT_EULER_1_1 | Explicit Euler |
| Midpoint-2-2 | dg::MIDPOINT_2_2 | Midpoint method |
| Kutta-3-3 | dg::KUTTA_3_3 | Kutta-3-3 |
| Runge-Kutta-4-4 | dg::CLASSIC_4_4 | "The" Runge-Kutta method |
| SSPRK-2-2 | dg::SSPRK_2_2 | SSPRK (2,2) CFL_eff = 0.5 "Shu-Osher-Form" |
| SSPRK-3-2 | dg::SSPRK_3_2 | SSPRK (3,2) CFL_eff = 0.66 "Shu-Osher-Form" |
| SSPRK-3-3 | dg::SSPRK_3_3 | SSPRK (3,3) CFL_eff = 0.33 "Shu-Osher-Form" |
| SSPRK-5-3 | dg::SSPRK_5_3 | SSPRK (5,3) CFL_eff = 0.5 "Shu-Osher-Form" |
| SSPRK-5-4 | dg::SSPRK_5_4 | SSPRK (5,4) CFL_eff = 0.37 "Shu-Osher-Form" |
| Heun-Euler-2-1-2 | dg::HEUN_EULER_2_1_2 | Heun-Euler-2-1-2 |
| Cavaglieri-3-1-2 (explicit) | dg::CAVAGLIERI_3_1_2 | Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems IMEXRKCB2 scheme |
| Fehlberg-3-2-3 | dg::FEHLBERG_3_2_3 | The original uses the embedding as the solution [Hairer, Noersett, Wanner, Solving ordinary differential Equations I, 1987] |
| Fehlberg-4-2-3 | dg::FEHLBERG_4_2_3 | The original uses the embedding as the solution [Hairer, Noersett, Wanner, Solving ordinary differential Equations I, 1987] (fsal) |
| Bogacki-Shampine-4-2-3 | dg::BOGACKI_SHAMPINE_4_2_3 | Bogacki-Shampine (fsal) |
| Cavaglieri-4-2-3 (explicit) | dg::CAVAGLIERI_4_2_3 | Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems The SSP scheme IMEXRKCB3c (explicit part) |
| ARK-4-2-3 (explicit) | dg::ARK324L2SA_ERK_4_2_3 | ARK-4-2-3 (explicit) |
| Zonneveld-5-3-4 | dg::ZONNEVELD_5_3_4 | Zonneveld-5-3-4 |
| ARK-6-3-4 (explicit) | dg::ARK436L2SA_ERK_6_3_4 | ARK-6-3-4 (explicit) |
| Sayfy_Aburub-6-3-4 | dg::SAYFY_ABURUB_6_3_4 | Sayfy_Aburub_6_3_4 |
| Cash_Karp-6-4-5 | dg::CASH_KARP_6_4_5 | Cash-Karp |
| Fehlberg-6-4-5 | dg::FEHLBERG_6_4_5 | Runge-Kutta-Fehlberg |
| Dormand-Prince-7-4-5 | dg::DORMAND_PRINCE_7_4_5 | Dormand-Prince method (fsal) |
| Tsitouras09-7-4-5 | dg::TSITOURAS09_7_4_5 | Tsitouras 5(4) method from 2009 (fsal), The default method in Julia |
| Tsitouras11-7-4-5 | dg::TSITOURAS11_7_4_5 | Tsitouras 5(4) method from 2011 (fsal) Further improves Tsitouras09 (Note that in the paper b-bt is printed instead of bt) |
| ARK-8-4-5 (explicit) | dg::ARK548L2SA_ERK_8_4_5 | Kennedy and Carpenter (2019) Optimum ARK_2 method (explicit part) |
| Verner-9-5-6 | dg::VERNER_9_5_6 | Verner-9-5-6 (fsal) |
| Verner-10-6-7 | dg::VERNER_10_6_7 | Verner-10-6-7 |
| Fehlberg-13-7-8 | dg::FEHLBERG_13_7_8 | Fehlberg-13-7-8 |
| Dormand-Prince-13-7-8 | dg::DORMAND_PRINCE_13_7_8 | [Hairer, Noersett, Wanner, Solving ordinary differential Equations I, 1987] |
| Feagin-17-8-10 | dg::FEAGIN_17_8_10 | Feagin (The RK10(8) method) |
- Note
- A Shu-Osher Tableau can be uniquely converted to a ButcherTableau but the converse is not true
- Template Parameters
-
| real_type | type of the coefficients |
- See also
- ShuOsher
◆ value_type
template<class real_type >
◆ ShuOsherTableau() [1/2]
template<class real_type >
◆ ShuOsherTableau() [2/2]
template<class real_type >
| dg::ShuOsherTableau< real_type >::ShuOsherTableau |
( |
unsigned |
stages, |
|
|
unsigned |
order, |
|
|
const std::vector< real_type > & |
alpha_v, |
|
|
const std::vector< real_type > & |
beta_v |
|
) |
| |
|
inline |
Construct a non-embedded explicit tableau.
- Parameters
-
| stages | number of stages |
| order | (global) order of the resulting method |
| alpha_v | s*s/2 real numbers interpreted as a linearized triangle |
| beta_v | s*s/2 real numbers interpreted as a linearized triangle |
◆ alpha()
template<class real_type >
Read the alpha_ij coefficients.
- Parameters
-
| i | row number 0<=i<s, i>=s results in undefined behaviour |
| j | col number 0<=j<s, j>=s results in undefined behaviour |
- Returns
- alpha_ij
◆ beta()
template<class real_type >
Read the beta_ij coefficients.
- Parameters
-
| i | row number 0<=i<s, i>=s results in undefined behaviour |
| j | col number 0<=j<s, j>=s results in undefined behaviour |
- Returns
- beta_ij
◆ num_stages()
template<class real_type >
◆ operator ButcherTableau< real_type >()
template<class real_type >
A Shu-Osher Tableau can be converted to a Butcher table.
- Returns
- the corresponding Butcher Tableau
◆ order()
template<class real_type >
global order of accuracy for the method
The documentation for this struct was generated from the following file:
1.9.3