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Initial-Value Problems/RK tableaus/Hairer RK10(6) Pair.txt

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+Hairer's 10th-order Runge-Kutta method with a non-defective sixth order error estimator.
+
+References:
+[1] E. Hairer. (1975). "A Runge-Kutta Method of Order 10", Journal of the Institute of Mathematics and its Applications (1975) 16, pages 35 to 55.
+[2] P. Stone. (November 29, 2011). "Hairer's 17 stage order 10 Runge-Kutta scheme". Accessed on October 5, 2023 from http://www.peterstone.name/Maplepgs/Maple/nmthds/RKcoeff/Runge_Kutta_schemes/RK10/RKcoeff10b_1.pdf
+[3] Tsitouras, Charalampos & Papakostas, S.. (1999). Cheap Error Estimation for Runge--Kutta Methods. Siam Journal on Scientific Computing. 20. 10.1137/S1064827596302230. 
+
+c[0] = 0.0
+c[1] = 0.52335840046200471396329370232151705
+c[2] = 0.52650910014161257273295167347754083
+c[3] = 0.78976365021241885909942751021631124
+c[4] = 0.39392357012567201432277381199965214
+c[5] = 0.76665398625355059119326686935606866
+c[6] = 0.28976365021241885909942751021631124
+c[7] = 0.10847768921956729335364611003962721
+c[8] = 0.35738424175967745184292450297956046
+c[9] = 0.88252766196473234642550148697966908
+c[10] = 0.64261575824032254815707549702043954
+c[11] = 0.11747233803526765357449851302033092
+c[12] = 0.76665398625355059119326686935606866
+c[13] = 0.28976365021241885909942751021631124
+c[14] = 0.52650910014161257273295167347754083
+c[15] = 0.52335840046200471396329370232151705
+c[16] = 1.0
+c[17] = 1.1594751649181922776183076757103665
+
+a[1,0] = 0.52335840046200471396329370232151705
+
+a[2,0] = 0.26166971637781272833124020975489976
+a[2,1] = 0.26483938376379984440171146372264106
+
+a[3,0] = 0.19744091255310471477485687755407781
+a[3,1] = 0.0
+a[3,2] = 0.59232273765931414432457063266223343
+
+a[4,0] = 0.19732054862870230670366494859789521
+a[4,1] = 0.0
+a[4,2] = 0.29508333409267219182282555982743592
+a[4,3] = -0.098480312595702484203716696425678998
+
+a[5,0] = 0.13131341734446165361301779993459095
+a[5,1] = 0.0
+a[5,2] = 0.0
+a[5,3] = 0.11015443953863962067736969677168929
+a[5,4] = 0.52518612937044931690287937264978842
+
+a[6,0] = 0.13420034184632260027274769516809314
+a[6,1] = 0.0
+a[6,2] = 0.0
+a[6,3] = 0.69608870328811608022998240476783148
+a[6,4] = 0.25049772157033980971255180925098002
+a[6,5] = -0.79102311649235963111585439897059341
+
+a[7,0] = 0.072218274189662619420050818455170498
+a[7,1] = 0.0
+a[7,2] = 0.0
+a[7,3] = 0.0
+a[7,4] = -0.058336322936456107163806061389306519
+a[7,5] = 0.0030475576685745252201749500702940361
+a[7,6] = 0.091548180297786255877226402903469198
+
+a[8,0] = 0.031255008135166179470501205282634766
+a[8,1] = 0.0
+a[8,2] = 0.0
+a[8,3] = 0.0
+a[8,4] = 0.0
+a[8,5] = 0.00010912382154241289292948349552077165
+a[8,6] = 0.15672575863099383562461074656487947
+a[8,7] = 0.16929435117197502385488306763652546
+
+a[9,0] = 0.011906604414668619242168842580809251
+a[9,1] = 0.0
+a[9,2] = 0.0
+a[9,3] = 0.0
+a[9,4] = 0.0
+a[9,5] = 0.28343708202460278602559922669821887
+a[9,6] = -0.41631216757062823537242761813563002
+a[9,7] = 0.2646463339497663668210902091085361
+a[9,8] = 0.73884980914632280970907082672773488
+
+a[10,0] = 0.023406573691331978914708383779840078
+a[10,1] = 0.0
+a[10,2] = 0.0
+a[10,3] = 0.0
+a[10,4] = 0.0
+a[10,5] = 0.094493130189493654013002530956056143
+a[10,6] = -0.27287205590199526063630925806659632
+a[10,7] = 0.22402204611560579979443155225181318
+a[10,8] = 0.60438144107516575697193472225760853
+a[10,9] = -0.030815376929279380900692434158282079
+
+a[11,0] = 0.045443775310176163157653899081530965
+a[11,1] = 0.0
+a[11,2] = 0.0
+a[11,3] = 0.0
+a[11,4] = 0.0
+a[11,5] = -0.0011879966718640285867652542192853563
+a[11,6] = 0.012035654990922610979661882172343621
+a[11,7] = 0.075126902987649668216275213715655721
+a[11,8] = -0.018220924098880124031411861059748389
+a[11,9] = -0.00025715285408410434688063762217713962
+a[11,10] = 0.0045320783713474681859652709520115027
+
+a[12,0] = 0.17671377825927720309587987657119933
+a[12,1] = 0.0
+a[12,2] = 0.0
+a[12,3] = 0.11015443953863962067736969677168929
+a[12,4] = 0.52518612937044931690287937264978842
+a[12,5] = -0.47162076728019579487982179121523594
+a[12,6] = 0.89903104984918752663689900718751529
+a[12,7] = -0.74672303069162896385996020080881681
+a[12,8] = -1.017101516756146040853186972006066
+a[12,9] = 0.12635087151959889629513078276876483
+a[12,10] = 0.566013827235506427068273224990747
+a[12,11] = 0.59864920520886240010980387244648321
+
+a[13,0] = 0.12775349474808698226947770068805715
+a[13,1] = 0.0
+a[13,2] = 0.0
+a[13,3] = 0.69608870328811608022998240476783148
+a[13,4] = 0.25049772157033980971255180925098002
+a[13,5] = -0.73682464360284168676092467574545354
+a[13,6] = -0.27785787771082418267732733749007233
+a[13,7] = -0.5997526313598403501296884799197753
+a[13,8] = 0.20246923389107046935002375856219031
+a[13,9] = 0.0054320369823638497806006846526344436
+a[13,10] = -0.010744724741550479201012069198943813
+a[13,11] = 0.69516884845702340047005918581641461
+a[13,12] = -0.062466511309525033944315471167551805
+
+a[14,0] = 0.26166971637781272833124020975489976
+a[14,1] = 0.26483938376379984440171146372264106
+a[14,2] = 0.0
+a[14,3] = 0.0
+a[14,4] = 0.0
+a[14,5] = -0.1998011270205324791079663580830885
+a[14,6] = -0.65104998730528271249219144896838136
+a[14,7] = 0.0
+a[14,8] = 0.0
+a[14,9] = 0.0
+a[14,10] = 0.0
+a[14,11] = 0.0
+a[14,12] = 0.1998011270205324791079663580830885
+a[14,13] = 0.65104998730528271249219144896838136
+
+a[15,0] = 0.52335840046200471396329370232151705
+a[15,1] = 0.0
+a[15,2] = -0.55588121367543020607261431053092935
+a[15,3] = 0.0
+a[15,4] = 0.0
+a[15,5] = 0.0
+a[15,6] = 0.0
+a[15,7] = 0.0
+a[15,8] = 0.0
+a[15,9] = 0.0
+a[15,10] = 0.0
+a[15,11] = 0.0
+a[15,12] = 0.0
+a[15,13] = 0.0
+a[15,14] = 0.55588121367543020607261431053092935
+
+a[16,0] = 0.057320795432065591031142617051039837
+a[16,1] = -0.54997107638999456081158418962901879
+a[16,2] = -0.64993741740087491351166074200108906
+a[16,3] = 0.0
+a[16,4] = 0.0
+a[16,5] = -1.0616673704017562072400195390231571
+a[16,6] = -0.040401566898063582942696822342121833
+a[16,7] = -0.1828302366407607254710272774065261
+a[16,8] = -0.33365927064927868456665756618281627
+a[16,9] = 0.39564854237605675688013451071660155
+a[16,10] = 0.69505704945997358910020992820051581
+a[16,11] = 0.27148737645737485883772630585392209
+a[16,12] = 0.60718105604140412028737743497946802
+a[16,13] = 0.59186362482298428408381040815307397
+a[16,14] = 0.64993741740087491351166074200108906
+a[16,15] = 0.54997107638999456081158418962901879
+
+a[17,0] = 0.12445832373808099546998998797622129
+a[17,1] = 0.0
+a[17,2] = 0.0
+a[17,3] = 0.11623459471215480044491475631609553
+a[17,4] = 0.55832690162183036227975081779574614
+a[17,5] = 0.0
+a[17,6] = 0.0
+a[17,7] = 0.0
+a[17,8] = 0.0
+a[17,9] = 0.0
+a[17,10] = 0.0
+a[17,11] = 0.0
+a[17,12] = 0.0
+a[17,13] = 0.0
+a[17,14] = 0.0
+a[17,15] = 0.0
+a[17,16] = 0.36045534484612611942365211362230357
+
+#-------------------------------------------------------------
+# 10th order weights
+#-------------------------------------------------------------
+b[0] = 0.033333333333333333333333333333333333
+b[1] = -0.038461538461538461538461538461538462
+b[2] = -0.090909090909090909090909090909090909
+b[3] = 0.0
+b[4] = 0.0
+b[5] = -0.13483146067415730337078651685393258
+b[6] = -0.11111111111111111111111111111111111
+b[7] = 0.0
+b[8] = 0.27742918851774317650836026256065434
+b[9] = 0.18923747814892349015830640410601233
+b[10] = 0.27742918851774317650836026256065434
+b[11] = 0.18923747814892349015830640410601233
+b[12] = 0.13483146067415730337078651685393258
+b[13] = 0.11111111111111111111111111111111111
+b[14] = 0.090909090909090909090909090909090909
+b[15] = 0.038461538461538461538461538461538462
+b[16] = 0.033333333333333333333333333333333333
+b[17] = 0.0
+
+#-------------------------------------------------------------
+# error estimate weights
+#-------------------------------------------------------------
+e[0] = 0.0060297571692564621722799331362330804
+e[1] = 0.038461538461538461538461538461538462
+e[2] = 0.090909090909090909090909090909090909
+e[3] = 0.0
+e[4] = 0.0
+e[5] = -0.056764326225521868106559369607701955
+e[6] = -0.18983144062669067936808485167146244
+e[7] = 0.050286310012688216133291262963052085
+e[8] = 0.035526756062761030620281514414646974
+e[9] = 0.083307505130064307222044846510252782
+e[10] = -0.049976293276353439121117740932562913
+e[11] = -0.070570219448782434710246067933407669
+e[12] = 0.052168539325842696629213483146067416
+e[13] = 0.18888888888888888888888888888888889
+e[14] = -0.090909090909090909090909090909090909
+e[15] = -0.038461538461538461538461538461538462
+e[16] = -0.059065477012153180359991898914006248
+e[17] = 0.01