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path: root/rk1210.txt
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                     THE COEFFICIENTS OF RK12(10) TO 60 DIGITS
             using the notation of Fehlberg, Bettis, Horn, et alia

  k				a[k]

  0    0.000000000000000000000000000000000000000000000000000000000000
  1    0.200000000000000000000000000000000000000000000000000000000000
  2    0.555555555555555555555555555555555555555555555555555555555556
  3    0.833333333333333333333333333333333333333333333333333333333333
  4    0.333333333333333333333333333333333333333333333333333333333333
  5    1.00000000000000000000000000000000000000000000000000000000000
  6    0.671835709170513812712245661002797570438953420568682550710222
  7    0.288724941110620201935458488967024976908118598341806976469674
  8    0.562500000000000000000000000000000000000000000000000000000000
  9    0.833333333333333333333333333333333333333333333333333333333333
 10    0.947695431179199287562380162101836721649589325892740646458322
 11    0.0548112876863802643887753674810754475842153612931128785028369
 12    0.0848880518607165350639838930162674302064148175640019542045934
 13    0.265575603264642893098114059045616835297201264164077621448665
 14    0.500000000000000000000000000000000000000000000000000000000000
 15    0.734424396735357106901885940954383164702798735835922378551335
 16    0.915111948139283464936016106983732569793585182435998045795407
 17    0.947695431179199287562380162101836721649589325892740646458322
 18    0.833333333333333333333333333333333333333333333333333333333333
 19    0.288724941110620201935458488967024976908118598341806976469674
 20    0.671835709170513812712245661002797570438953420568682550710222
 21    0.333333333333333333333333333333333333333333333333333333333333
 22    0.555555555555555555555555555555555555555555555555555555555556
 23    0.200000000000000000000000000000000000000000000000000000000000
 24    1.00000000000000000000000000000000000000000000000000000000000  

  k				c[k]

  0    0.0238095238095238095238095238095238095238095238095238095238095
  1    0.0234375000000000000000000000000000000000000000000000000000000
  2    0.0312500000000000000000000000000000000000000000000000000000000
  3    0.000000000000000000000000000000000000000000000000000000000000
  4    0.0416666666666666666666666666666666666666666666666666666666667
  5    0.000000000000000000000000000000000000000000000000000000000000
  6    0.0500000000000000000000000000000000000000000000000000000000000
  7    0.0500000000000000000000000000000000000000000000000000000000000
  8    0.000000000000000000000000000000000000000000000000000000000000
  9    0.100000000000000000000000000000000000000000000000000000000000
 10    0.0714285714285714285714285714285714285714285714285714285714286
 11    0.000000000000000000000000000000000000000000000000000000000000
 12    0.138413023680782974005350203145033146748813640089941234591267
 13    0.215872690604931311708935511140681138965472074195773051123019
 14    0.243809523809523809523809523809523809523809523809523809523810
 15    0.215872690604931311708935511140681138965472074195773051123019
 16    0.138413023680782974005350203145033146748813640089941234591267
 17   -0.0714285714285714285714285714285714285714285714285714285714286
 18   -0.100000000000000000000000000000000000000000000000000000000000
 19   -0.0500000000000000000000000000000000000000000000000000000000000
 20   -0.0500000000000000000000000000000000000000000000000000000000000
 21   -0.0416666666666666666666666666666666666666666666666666666666667
 22   -0.0312500000000000000000000000000000000000000000000000000000000
 23   -0.0234375000000000000000000000000000000000000000000000000000000
 24    0.0238095238095238095238095238095238095238095238095238095238095

 
  k    j				ß[k,j] 

  1    0    0.200000000000000000000000000000000000000000000000000000000000
  2    0   -0.216049382716049382716049382716049382716049382716049382716049
  2    1    0.771604938271604938271604938271604938271604938271604938271605
  3    0    0.208333333333333333333333333333333333333333333333333333333333
  3    1    0.000000000000000000000000000000000000000000000000000000000000
  3    2    0.625000000000000000000000000000000000000000000000000000000000
  4    0    0.193333333333333333333333333333333333333333333333333333333333
  4    1    0.000000000000000000000000000000000000000000000000000000000000
  4    2    0.220000000000000000000000000000000000000000000000000000000000
  4    3   -0.0800000000000000000000000000000000000000000000000000000000000
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  6    0    0.103364471650010477570395435690481791543342708330349879244197
  6    1    0.000000000000000000000000000000000000000000000000000000000000
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  6    3    0.124053094528946761061581889237115328211074784955180298044074
  6    4    0.483171167561032899288836480451962508724109257517289177302380
  6    5   -0.0387530245694763252085681443767620580395733302341368038804290
  7    0    0.124038261431833324081904585980175168140024670698633612292480
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  7    4    0.217050632197958486317846256953159942875916353757734167684657
  7    5    0.0137455792075966759812907801835048190594443990939408530842918
  7    6   -0.0661095317267682844455831341498149531672668252085016565917546
  8    0    0.0914774894856882983144991846980432197088832099976660100090486
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  8    5   -0.00544348523717469689965754944144838611346156873847009178068318
  8    6    0.0680716801688453518578515120895103863112751730758794372203952
  8    7    0.408394315582641046727306852653894780093303185664924644551239
  9    0    0.0890013652502551018954509355423841780143232697403434118692699
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  9    5    0.00499528226645532360197793408420692800405891149406814091955810
  9    6    0.397918238819828997341739603001347156083435060931424970826304
  9    7    0.427930210752576611068192608300897981558240730580396406312359
  9    8   -0.0865117637557827005740277475955029103267246394128995965941585
 10    0    0.0695087624134907543112693906409809822706021061685544615255758
 10    1    0.000000000000000000000000000000000000000000000000000000000000
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 10    5    0.129146941900176461970759579482746551122871751501482634045487
 10    6    1.53073638102311295076342566143214939031177504112433874313011
 10    7    0.577874761129140052546751349454576715334892100418571882718036
 10    8   -0.951294772321088980532340837388859453930924498799228648050949
 10    9   -0.408276642965631951497484981519757463459627174520978426909934
 11    0    0.0444861403295135866269453507092463581620165501018684152933313
 11    1    0.000000000000000000000000000000000000000000000000000000000000
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 11    5   -0.00380476867056961731984232686574547203016331563626856065717964
 11    6    0.0106955064029624200721262602809059154469206077644957399593972
 11    7    0.0209616244499904333296674205928919920806734650660039898074652
 11    8   -0.0233146023259321786648561431551978077665337818756053603898847
 11    9    0.00263265981064536974369934736325334761174975280887405725010964
 11   10    0.00315472768977025060103545855572111407955208306374459723959783
 12    0    0.0194588815119755475588801096525317761242073762016273186231215
 12    1    0.000000000000000000000000000000000000000000000000000000000000
 12    2    0.000000000000000000000000000000000000000000000000000000000000
 12    3    0.000000000000000000000000000000000000000000000000000000000000
 12    4    0.000000000000000000000000000000000000000000000000000000000000
 12    5    0.000000000000000000000000000000000000000000000000000000000000
 12    6    0.000000000000000000000000000000000000000000000000000000000000
 12    7    0.000000000000000000000000000000000000000000000000000000000000
 12    8    0.0000678512949171812509306121653452367476194364781259165332321534
 12    9   -0.0000429795859049273623271005330230162343568863387724883603675550
 12   10    0.0000176358982260285155407485928953302139937553442829975734148981
 12   11    0.0653866627415027051009595231385181033549511358787382098351924
 13    0    0.206836835664277105916828174798272361078909196043446411598231
 13    1    0.000000000000000000000000000000000000000000000000000000000000
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 13    6    0.000000000000000000000000000000000000000000000000000000000000
 13    7    0.000000000000000000000000000000000000000000000000000000000000
 13    8    0.0166796067104156472828045866664696450306326505094792505215514
 13    9   -0.00879501563200710214457024178249986591130234990219959208704979
 13   10    0.00346675455362463910824462315246379209427513654098596403637231
 13   11   -0.861264460105717678161432562258351242030270498966891201799225
 13   12    0.908651882074050281096239478469262145034957129939256789178785
 14    0    0.0203926084654484010091511314676925686038504449562413004562382
 14    1    0.000000000000000000000000000000000000000000000000000000000000
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 14    8    0.0869469392016685948675400555583947505833954460930940959577347
 14    9   -0.0191649630410149842286436611791405053287170076602337673587681
 14   10    0.00655629159493663287364871573244244516034828755253746024098838
 14   11    0.0987476128127434780903798528674033899738924968006632201445462
 14   12    0.00535364695524996055083260173615567408717110247274021056118319
 14   13    0.301167864010967916837091303817051676920059229784957479998077
 15    0    0.228410433917778099547115412893004398779136994596948545722283
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 15    8   -0.498707400793025250635016567442511512138603770959682292383042
 15    9    0.134841168335724478552596703792570104791700727205981058201689
 15   10   -0.0387458244055834158439904226924029230935161059142806805674360
 15   11   -1.27473257473474844240388430824908952380979292713250350199641
 15   12    1.43916364462877165201184452437038081875299303577911839630524
 15   13   -0.214007467967990254219503540827349569639028092344812795499026
 15   14    0.958202417754430239892724139109781371059908874605153648768037
 16    0    2.00222477655974203614249646012506747121440306225711721209798
 16    1    0.000000000000000000000000000000000000000000000000000000000000
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 16    6    0.000000000000000000000000000000000000000000000000000000000000
 16    7    0.000000000000000000000000000000000000000000000000000000000000
 16    8    2.06701809961524912091954656438138595825411859673341600679555
 16    9    0.623978136086139541957471279831494466155292316167021080663140
 16   10   -0.0462283685500311430283203554129062069391947101880112723185773
 16   11   -8.84973288362649614860075246727118949286604835457092701094630
 16   12    7.74257707850855976227437225791835589560188590785037197433615
 16   13   -0.588358519250869210993353314127711745644125882130941202896436
 16   14   -1.10683733362380649395704708016953056176195769617014899442903
 16   15   -0.929529037579203999778397238291233214220788057511899747507074
 17    0    3.13789533412073442934451608989888796808161259330322100268310
 17    1    0.000000000000000000000000000000000000000000000000000000000000
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 17    3    0.000000000000000000000000000000000000000000000000000000000000
 17    4    0.000000000000000000000000000000000000000000000000000000000000
 17    5    0.129146941900176461970759579482746551122871751501482634045487
 17    6    1.53073638102311295076342566143214939031177504112433874313011
 17    7    0.577874761129140052546751349454576715334892100418571882718036
 17    8    5.42088263055126683050056840891857421941300558851862156403363
 17    9    0.231546926034829304872663800877643660904880180835945693836936
 17   10    0.0759292995578913560162301311785251873561801342333194895292058
 17   11  -12.3729973380186513287414553402595806591349822617535905976253
 17   12    9.85455883464769543935957209317369202080367765721777101906955
 17   13    0.0859111431370436529579357709052367772889980495122329601159540
 17   14   -5.65242752862643921117182090081762761180392602644189218673969
 17   15   -1.94300935242819610883833776782364287728724899124166920477873
 17   16   -0.128352601849404542018428714319344620742146491335612353559923
 18    0    1.38360054432196014878538118298167716825163268489922519995564
 18    1    0.000000000000000000000000000000000000000000000000000000000000
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 18    5    0.00499528226645532360197793408420692800405891149406814091955810
 18    6    0.397918238819828997341739603001347156083435060931424970826304
 18    7    0.427930210752576611068192608300897981558240730580396406312359
 18    8   -1.30299107424475770916551439123047573342071475998399645982146
 18    9    0.661292278669377029097112528107513072734573412294008071500699
 18   10   -0.144559774306954349765969393688703463900585822441545655530145
 18   11   -6.96576034731798203467853867461083919356792248105919255460819
 18   12    6.65808543235991748353408295542210450632193197576935120716437
 18   13   -1.66997375108841486404695805725510845049807969199236227575796
 18   14    2.06413702318035263832289040301832647130604651223986452170089
 18   15   -0.674743962644306471862958129570837723192079875998405058648892
 18   16   -0.00115618834794939500490703608435907610059605754935305582045729
 18   17   -0.00544057908677007389319819914241631024660726585015012485938593
 19    0    0.951236297048287669474637975894973552166903378983475425758226
 19    1    0.000000000000000000000000000000000000000000000000000000000000
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 19    4    0.217050632197958486317846256953159942875916353757734167684657
 19    5    0.0137455792075966759812907801835048190594443990939408530842918
 19    6   -0.0661095317267682844455831341498149531672668252085016565917546
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 19    8    0.152281696736414447136604697040747131921486432699422112099617
 19    9   -0.337741018357599840802300793133998004354643424457539667670080
 19   10   -0.0192825981633995781534949199286824400469353110630787982121133
 19   11   -3.68259269696866809932409015535499603576312120746888880201882
 19   12    3.16197870406982063541533528419683854018352080342887002331312
 19   13   -0.370462522106885290716991856022051125477943482284080569177386
 19   14   -0.0514974200365440434996434456698127984941168616474316871020314
 19   15   -0.000829625532120152946787043541792848416659382675202720677536554
 19   16    0.00000279801041419278598986586589070027583961355402640879503213503
 19   17    0.0418603916412360287969841020776788461794119440689356178942252
 19   18    0.279084255090877355915660874555379649966282167560126269290222
 20    0    0.103364471650010477570395435690481791543342708330349879244197
 20    1    0.000000000000000000000000000000000000000000000000000000000000
 20    2    0.000000000000000000000000000000000000000000000000000000000000
 20    3    0.124053094528946761061581889237115328211074784955180298044074
 20    4    0.483171167561032899288836480451962508724109257517289177302380
 20    5   -0.0387530245694763252085681443767620580395733302341368038804290
 20    6    0.000000000000000000000000000000000000000000000000000000000000
 20    7   -0.438313820361122420391059788940960176420682836652600698580091
 20    8    0.000000000000000000000000000000000000000000000000000000000000
 20    9   -0.218636633721676647685111485017151199362509373698288330593486
 20   10   -0.0312334764394719229981634995206440349766174759626578122323015
 20   11    0.000000000000000000000000000000000000000000000000000000000000
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 20   17    0.0312334764394719229981634995206440349766174759626578122323015
 20   18    0.218636633721676647685111485017151199362509373698288330593486
 20   19    0.438313820361122420391059788940960176420682836652600698580091
 21    0    0.193333333333333333333333333333333333333333333333333333333333
 21    1    0.000000000000000000000000000000000000000000000000000000000000
 21    2    0.220000000000000000000000000000000000000000000000000000000000
 21    3   -0.0800000000000000000000000000000000000000000000000000000000000
 21    4    0.000000000000000000000000000000000000000000000000000000000000
 21    5    0.000000000000000000000000000000000000000000000000000000000000
 21    6    0.0984256130499315928152900286856048243348202521491288575952143
 21    7   -0.196410889223054653446526504390100417677539095340135532418849
 21    8    0.000000000000000000000000000000000000000000000000000000000000
 21    9    0.436457930493068729391826122587949137609670676712525034763317
 21   10    0.0652613721675721098560370939805555698350543810708414716730270
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 21   18   -0.436457930493068729391826122587949137609670676712525034763317
 21   19    0.196410889223054653446526504390100417677539095340135532418849
 21   20   -0.0984256130499315928152900286856048243348202521491288575952143
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 22   21    0.666666666666666666666666666666666666666666666666666666666667
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 23   22    0.164609053497942386831275720164609053497942386831275720164609
 24    0    1.47178724881110408452949550989023611293535315518571691939396
 24    1    0.787500000000000000000000000000000000000000000000000000000000
 24    2    0.421296296296296296296296296296296296296296296296296296296296
 24    3    0.000000000000000000000000000000000000000000000000000000000000
 24    4    0.291666666666666666666666666666666666666666666666666666666667
 24    5    0.000000000000000000000000000000000000000000000000000000000000
 24    6    0.348600717628329563206854421629657569274689947367847465753757
 24    7    0.229499544768994849582890233710555447073823569666506700662510
 24    8    5.79046485790481979159831978177003471098279506036722411333192
 24    9    0.418587511856506868874073759426596207226461447604248151080016
 24   10    0.307039880222474002649653817490106690389251482313213999386651
 24   11   -4.68700905350603332214256344683853248065574415794742040470287
 24   12    3.13571665593802262152038152399873856554395436199962915429076
 24   13    1.40134829710965720817510506275620441055845017313930508348898
 24   14   -5.52931101439499023629010306005764336421276055777658156400910
 24   15   -0.853138235508063349309546894974784906188927508039552519557498
 24   16    0.103575780373610140411804607167772795518293914458500175573749
 24   17   -0.140474416950600941142546901202132534870665923700034957196546
 24   18   -0.418587511856506868874073759426596207226461447604248151080016
 24   19   -0.229499544768994849582890233710555447073823569666506700662510
 24   20   -0.348600717628329563206854421629657569274689947367847465753757
 24   21   -0.291666666666666666666666666666666666666666666666666666666667
 24   22   -0.421296296296296296296296296296296296296296296296296296296296
 24   23   -0.787500000000000000000000000000000000000000000000000000000000

 The estimate of the local truncation error is  (49/640)  h ( f(t1,x1)-f(t23,x23) )