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      + + +
      +[docs] +class ARK548L2SAESDIRK2(RungeKutta): + """ + Stiffly accurate singly diagonally L-stable implicit embedded Runge-Kutta pair of orders 5 and 4 with explicit first stage from [here](https://doi.org/10.1016/j.apnum.2018.10.007). + This method is part of the IMEX method ARK548L2SA. + """ + + ButcherTableauClass = ButcherTableauEmbedded + gamma = 2.0 / 9.0 + nodes = np.array( + [ + 0.0, + 4.0 / 9.0, + 6456083330201.0 / 8509243623797.0, + 1632083962415.0 / 14158861528103.0, + 6365430648612.0 / 17842476412687.0, + 18.0 / 25.0, + 191.0 / 200.0, + 1.0, + ] + ) + + weights = np.array( + [ + [ + 0.0, + 0.0, + 3517720773327.0 / 20256071687669.0, + 4569610470461.0 / 17934693873752.0, + 2819471173109.0 / 11655438449929.0, + 3296210113763.0 / 10722700128969.0, + -1142099968913.0 / 5710983926999.0, + gamma, + ], + [ + 0.0, + 0.0, + 520639020421.0 / 8300446712847.0, + 4550235134915.0 / 17827758688493.0, + 1482366381361.0 / 6201654941325.0, + 5551607622171.0 / 13911031047899.0, + -5266607656330.0 / 36788968843917.0, + 1074053359553.0 / 5740751784926.0, + ], + ] + ) + + matrix = np.zeros((8, 8)) + matrix[2, 1] = 2366667076620.0 / 8822750406821.0 + matrix[3, 1] = -257962897183.0 / 4451812247028.0 + matrix[3, 2] = 128530224461.0 / 14379561246022.0 + matrix[4, 1] = -486229321650.0 / 11227943450093.0 + matrix[4, 2] = -225633144460.0 / 6633558740617.0 + matrix[4, 3] = 1741320951451.0 / 6824444397158.0 + matrix[5, 1] = 621307788657.0 / 4714163060173.0 + matrix[5, 2] = -125196015625.0 / 3866852212004.0 + matrix[5, 3] = 940440206406.0 / 7593089888465.0 + matrix[5, 4] = 961109811699.0 / 6734810228204.0 + matrix[6, 1] = 2036305566805.0 / 6583108094622.0 + matrix[6, 2] = -3039402635899.0 / 4450598839912.0 + matrix[6, 3] = -1829510709469.0 / 31102090912115.0 + matrix[6, 4] = -286320471013.0 / 6931253422520.0 + matrix[6, 5] = 8651533662697.0 / 9642993110008.0 + + for i in range(matrix.shape[0]): + matrix[i, i] = gamma + matrix[i, 0] = matrix[i, 1] + matrix[7, i] = weights[0][i] + +
      +[docs] + @classmethod + def get_update_order(cls): + return 5
      +
      + + + +
      +[docs] +class ARK548L2SAERK2(ARK548L2SAESDIRK2): + """ + Explicit embedded pair of Runge-Kutta methods of orders 5 and 4 from [here](https://doi.org/10.1016/j.apnum.2018.10.007). + This method is part of the IMEX method ARK548L2SA. + """ + + matrix = np.zeros((8, 8)) + matrix[2, 0] = 1.0 / 9.0 + matrix[2, 1] = 1183333538310.0 / 1827251437969.0 + matrix[3, 0] = 895379019517.0 / 9750411845327.0 + matrix[3, 1] = 477606656805.0 / 13473228687314.0 + matrix[3, 2] = -112564739183.0 / 9373365219272.0 + matrix[4, 0] = -4458043123994.0 / 13015289567637.0 + matrix[4, 1] = -2500665203865.0 / 9342069639922.0 + matrix[4, 2] = 983347055801.0 / 8893519644487.0 + matrix[4, 3] = 2185051477207.0 / 2551468980502.0 + matrix[5, 0] = -167316361917.0 / 17121522574472.0 + matrix[5, 1] = 1605541814917.0 / 7619724128744.0 + matrix[5, 2] = 991021770328.0 / 13052792161721.0 + matrix[5, 3] = 2342280609577.0 / 11279663441611.0 + matrix[5, 4] = 3012424348531.0 / 12792462456678.0 + matrix[6, 0] = 6680998715867.0 / 14310383562358.0 + matrix[6, 1] = 5029118570809.0 / 3897454228471.0 + matrix[6, 2] = 2415062538259.0 / 6382199904604.0 + matrix[6, 3] = -3924368632305.0 / 6964820224454.0 + matrix[6, 4] = -4331110370267.0 / 15021686902756.0 + matrix[6, 5] = -3944303808049.0 / 11994238218192.0 + matrix[7, 0] = 2193717860234.0 / 3570523412979.0 + matrix[7, 1] = 2193717860234.0 / 3570523412979.0 + matrix[7, 2] = 5952760925747.0 / 18750164281544.0 + matrix[7, 3] = -4412967128996.0 / 6196664114337.0 + matrix[7, 4] = 4151782504231.0 / 36106512998704.0 + matrix[7, 5] = 572599549169.0 / 6265429158920.0 + matrix[7, 6] = -457874356192.0 / 11306498036315.0 + + matrix[1, 0] = ARK548L2SAESDIRK2.nodes[1]
      + + + +
      +[docs] +class ARK548L2SA(RungeKuttaIMEX): + """ + IMEX Runge-Kutta method of order 5 based on the explicit method ARK548L2SAERK2 and the implicit method + ARK548L2SAESDIRK2 from [here](https://doi.org/10.1016/j.apnum.2018.10.007). + + According to Kennedy and Carpenter (see reference), the two IMEX RK methods of order 5 are the only ones available + as of now. And we are not aware of higher order ones. This one is newer then the other one and apparently better. + """ + + ButcherTableauClass = ButcherTableauEmbedded + ButcherTableauClass_explicit = ButcherTableauEmbedded + + nodes = ARK548L2SAERK2.nodes + weights = ARK548L2SAERK2.weights + + matrix = ARK548L2SAESDIRK2.matrix + matrix_explicit = ARK548L2SAERK2.matrix + +
      +[docs] + @classmethod + def get_update_order(cls): + return 5
      +
      +
      diff --git a/coverage/coverage-badge.svg b/coverage/coverage-badge.svg index 7b22408453..704abd5d41 100644 --- a/coverage/coverage-badge.svg +++ b/coverage/coverage-badge.svg @@ -1 +1 @@ -coverage: 72.99%coverage72.99% \ No newline at end of file +coverage: 73.07%coverage73.07% \ No newline at end of file diff --git a/coverage/d_020efe120a771d8a_fput_py.html b/coverage/d_020efe120a771d8a_fput_py.html index 83295b4d7b..12c2ddf3e8 100644 --- a/coverage/d_020efe120a771d8a_fput_py.html +++ b/coverage/d_020efe120a771d8a_fput_py.html @@ -65,7 +65,7 @@

      » next       coverage.py v7.3.1, - created at 2023-09-18 15:15 +0000 + created at 2023-09-19 14:10 +0000

      - 295 statements   - + 363 statements   +

      @@ -65,7 +65,7 @@

      » next       coverage.py v7.3.1, - created at 2023-09-18 15:15 +0000 + created at 2023-09-19 14:10 +0000

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