Butcher's tables type. The last number in the name always means order, the one before last (if provided) is the number of stages.
Enumerator |
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Explicit_RK_1 |
Explicit Runge-Kutta RK-1 (explicit Euler).
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Explicit_RK_2 |
Explicit Runge-Kutta RK-2 method.
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Explicit_RK_3 |
Explicit Runge-Kutta RK-3 method.
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Explicit_RK_4 |
Explicit Runge-Kutta RK-4 method.
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Implicit_RK_1 |
Implicit Runge-Kutta RK-1 (implicit Euler).
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Implicit_Crank_Nicolson_2_2 |
Implicit Crank_Nicolson method.
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Implicit_SIRK_2_2 |
Implicit SIRK-2-2 method.
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Implicit_ESIRK_2_2 |
Implicit ESIRK-2-2 method.
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Implicit_SDIRK_2_2 |
Implicit SDIRK-2-2 method.
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Implicit_Lobatto_IIIA_2_2 |
Implicit Lobatto IIIA-2 method.
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Implicit_Lobatto_IIIB_2_2 |
Implicit Lobatto IIIB-2 method.
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Implicit_Lobatto_IIIC_2_2 |
Implicit Lobatto IIIB-2 method.
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Implicit_Lobatto_IIIA_3_4 |
Implicit Lobatto IIIA-4 method.
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Implicit_Lobatto_IIIB_3_4 |
Implicit Lobatto IIIB-4 method.
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Implicit_Lobatto_IIIC_3_4 |
Implicit Lobatto IIIB-4 method.
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Implicit_Radau_IIA_3_5 |
Implicit Radau IIA-5 method.
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Implicit_SDIRK_5_4 |
Implicit SDIRK-5-4 method.
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Explicit_HEUN_EULER_2_12_embedded |
Heun-Euler (orders 1 and 2),.
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Explicit_BOGACKI_SHAMPINE_4_23_embedded |
Bogacki-Shampine (orders 2 and 3),.
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Explicit_FEHLBERG_6_45_embedded |
Fehlberg (orders 4 and 5),.
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Explicit_CASH_KARP_6_45_embedded |
Cash-Karp (orders 4 and 5),.
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Explicit_DORMAND_PRINCE_7_45_embedded |
Dormand-Prince (orders 4 and 5),.
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Implicit_ESDIRK_TRBDF2_3_23_embedded |
of TR-BDF2 by Hosea and Shampine.
From the paper Analysis and implementation
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Implicit_ESDIRK_TRX2_3_23_embedded |
of TR-BDF2 by Hosea and Shampine.
From the paper Analysis and implementation
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Implicit_SDIRK_CASH_3_23_embedded |
with Error Estimates by J.R. Cash
From the paper Diagonally Implicit Runge-Kutta Formulae
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Implicit_SDIRK_BILLINGTON_3_23_embedded |
Codes for the Solution of Stiff and Non-Stiff systems of ODE's.
From the Master Thesis by S.R. Billington: Type Insensitive
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Implicit_SDIRK_CASH_5_24_embedded |
with Error Estimates by J.R. Cash
From the paper Diagonally Implicit Runge-Kutta Formulae
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Implicit_SDIRK_CASH_5_34_embedded |
with Error Estimates by J.R. Cash
From the paper Diagonally Implicit Runge-Kutta Formulae
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Implicit_DIRK_ISMAIL_7_45_embedded |
Implicit embedded DIRK method pair of orders four in five (from the paper Fudziah Ismail et all: Embedded Pair of Diagonally Implicit Runge-Kutta Method for Solving Ordinary Differential Equations). The method has 7 stages but the first one is explicit.
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