Numerical/matrices.txt at master · ravenwit/Numerical · GitHub

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def Butcher_tableau(method):
    global a
    global b
    global c
    global F_i
    if method == 1:
        c = np.array([0, 1 / 2, 1 / 2, 1])
        a = np.array([
            [0, 0, 0, 0],
            [1 / 2, 0, 0, 0],
            [0, 1 / 2, 0, 0],
            [0, 0, 1, 0]
        ])
        b = np.array([1 / 6, 1 / 3, 1 / 3, 1 / 6])
    elif method==2:
        c = np.array([0,0.2,5/9,5/6,1/3,1,67801993/100920496,44758598/155021585,9/16,5/6,172135849/181636255,36851109/672327007,20592542/242584693,
                      30120495 / 113415896,1/2,210568577/286712394,96134905/105052617,172135849/181636255,5/6,44758598/155021585,67801993/100920496,1/3,5/9,1/5,1])
        a=np.array([
            [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
            [1/5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
            [-35/162, 125/162, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [5/24, 0, 5/8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [29/150, 0, 11/50, -2/25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [1/10, 0, 0, 2/5, 1/2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [37074941/358681667, 0, 0, 33585619/270735842, 257720006/533392767, -44020349/1135920344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [25230124/203405979, 0, 0, 0, 98101881/451976942, 65957727/4798468366, -6070937/91831493, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [24737624/270423075, 0, 0, 0, 0, -3736153/686353106, 19485332/286247261, 50525157/123716602, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [60247834/676931571, 0, 0, 0, 0, 4275247/855856941, 36672659/92161292, 16731755/39099261, -38981915/450596697, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [27288061/392584475, 0, 0, 0, 0, 365006343/2826287155, 141373675/92356644, 163264999/282526613, -51629527/54272901, 142621687/349326099, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [32856654/738581809, 0, 0, 0, 0, -14162705/3722356397, 25582922/2391931811, 51119620/2438724161, -25704425/1102503257, 4688654/1780957031, 3117485/988194642, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [10458484/537465835, 0, 0, 0, 0, 0, 0, 0, 296227/4365826774, -383576/8924609019, 146141/8286564037, 12646113/193405084, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [31431986/151965127, 0, 0, 0, 0, 0, 0, 0, 8107993/486102169, -20936474/2380493097, 11794237/3402097500, -152083614/176581783, 102389113/112682442, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [11253958/551864565, 0, 0, 0, 0, 0, 0, 0, 42975146/494268647, -4474701/233483414, 6268097/956043048, 15766372/159663323, 117183268/21888493765, 28144139/93450007, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [89861716/393422115, 0, 0, 0, 0, 0, 0, 0, -190920249/382830190, 37407972/277422485, -15879177/409829375, -24748163/19414396, 49033497/34070828,-135425641/632808015, 100437343/104818503, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [329422004/164527983, 0, 0, 0, 0, 0, 0, 0, 159202720/77020477, 152179118/243885337, -35567233/769381099, -466749240/52741619, 161194222/20819195, -453082123/770078291,-26419211/23869100,-79543028/85573473, 0, 0, 0, 0, 0, 0, 0, 0, 0],
            [121929017/38856942, 0, 0, 0, 0, 365006343/2826287155, 141373675/92356644, 163264999/282526613, 439144222/81009727, 13186261/56948547, 25264555/332737891, -401683667/32464540, 2492304541/252908789, 47761777/555943912, -75613337/13377144, -248933559/128117530, -36061621/280957460, 0, 0, 0, 0, 0, 0, 0, 0],
            [155993079/112744303, 0, 0, 0, 0, 4275247/855856941, 36672659/92161292,16731755/39099261, -164168531/125993596, 855875317/1294246651, -43179215/298694538, -509694778/73171449, 235461367/35364726, -82607643/49466432,119839851/58058089, -108798317/161243854,-1216233/1051933279, -11104923/2041128862, 0, 0, 0, 0, 0, 0, 0],
            [30575399/32142801, 0, 0, 0, 98101881/451976942, 65957727/4798468366, -6070937/91831493, 0, 58237611/382433426, -87760066/259844263, -9942595/515625276, -123996494/33670977, 101639181/32144170, -92687960/250195241, -4868661/94541843, -870114/1048803305,240782/86054719017,3179847/75963145,24618431/88211465, 0, 0, 0, 0, 0, 0],
            [37074941 / 358681667, 0, 0, 33585619 / 270735842, 257720006 / 533392767, -44020349 / 1135920344, 0,-120527899 / 274980832, 0, -58596715 / 268009592, -47102449 / 1508075769, 0, 0, 0, 0, 0, 0,47102449 / 1508075769, 58596715 / 268009592, 120527899 / 274980832, 0, 0, 0, 0, 0],
            [29/150, 0, 11/50, -2/25, 0,0, 14340957/145703507, -31420077/159971156, 0, 103497843/237131315, 22131167/339115870, 0, 0, 0, 0, 0, 0, -22131167/339115870, -103497843/237131315,31420077/159971156, -14340957/145703507, 0, 0, 0, 0],
            [-35/162, 125/162, 0, 0, -2/3, 0, -82382086/210859561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82382086/210859561,2/3, 0, 0, 0],
            [1/5, 0, -40/243, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40/243, 0, 0],
            [157084639/106730534, 63/80, 91/216, 0,7/24, 0, 100146079/287280186, 70568068/307486745,129515617/22367050,72807936/173937191, 51739211/168509742, -123960914/26447765 ,207695632/66235459, 222633283/158870770,-234969570/42495271, -108932901/127684936,28937867/279388356, -46373597/330121299, -72807936/173937191, -70568068/307486745, -100146079/287280186, -7/24, -91/216, -63/80, 0]
        ])
        b=np.array([1/42,3/128,1/32,0,1/24,0,1/20,1/20,0,1,1/14,0,38532146/278385263,
                    119008733/551291285,128/525,119008733/551291285,38532146/278385263,-1/14,
                    -1/10,-1/20,1/20,-1/24,-1/32,-3/128,1/42])
    F_i = np.array(np.zeros(len(b)))
    return a, b, c