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THE COEFFICIENTS OF RK10(8) TO 60 DIGITS
using the notation of Fehlberg, Bettis, Horn, et alia
k a[k]
0 0.000000000000000000000000000000000000000000000000000000000000
1 0.100000000000000000000000000000000000000000000000000000000000
2 0.539357840802981787532485197881302436857273449701009015505500
3 0.809036761204472681298727796821953655285910174551513523258250
4 0.309036761204472681298727796821953655285910174551513523258250
5 0.981074190219795268254879548310562080489056746118724882027805
6 0.833333333333333333333333333333333333333333333333333333333333
7 0.354017365856802376329264185948796742115824053807373968324184
8 0.882527661964732346425501486979669075182867844268052119663791
9 0.642615758240322548157075497020439535959501736363212695909875
10 0.357384241759677451842924502979560464040498263636787304090125
11 0.117472338035267653574498513020330924817132155731947880336209
12 0.833333333333333333333333333333333333333333333333333333333333
13 0.309036761204472681298727796821953655285910174551513523258250
14 0.539357840802981787532485197881302436857273449701009015505500
15 0.100000000000000000000000000000000000000000000000000000000000
16 1.00000000000000000000000000000000000000000000000000000000000
k c[k]
0 0.0333333333333333333333333333333333333333333333333333333333333
1 0.0250000000000000000000000000000000000000000000000000000000000
2 0.0333333333333333333333333333333333333333333333333333333333333
3 0.000000000000000000000000000000000000000000000000000000000000
4 0.0500000000000000000000000000000000000000000000000000000000000
5 0.000000000000000000000000000000000000000000000000000000000000
6 0.0400000000000000000000000000000000000000000000000000000000000
7 0.000000000000000000000000000000000000000000000000000000000000
8 0.189237478148923490158306404106012326238162346948625830327194
9 0.277429188517743176508360262560654340428504319718040836339472
10 0.277429188517743176508360262560654340428504319718040836339472
11 0.189237478148923490158306404106012326238162346948625830327194
12 -0.0400000000000000000000000000000000000000000000000000000000000
13 -0.0500000000000000000000000000000000000000000000000000000000000
14 -0.0333333333333333333333333333333333333333333333333333333333333
15 -0.0250000000000000000000000000000000000000000000000000000000000
16 0.0333333333333333333333333333333333333333333333333333333333333
k j ß[k,j]
1 0 0.100000000000000000000000000000000000000000000000000000000000
2 0 -0.915176561375291440520015019275342154318951387664369720564660
2 1 1.45453440217827322805250021715664459117622483736537873607016
3 0 0.202259190301118170324681949205488413821477543637878380814562
3 1 0.000000000000000000000000000000000000000000000000000000000000
3 2 0.606777570903354510974045847616465241464432630913635142443687
4 0 0.184024714708643575149100693471120664216774047979591417844635
4 1 0.000000000000000000000000000000000000000000000000000000000000
4 2 0.197966831227192369068141770510388793370637287463360401555746
4 3 -0.0729547847313632629185146671595558023015011608914382961421311
5 0 0.0879007340206681337319777094132125475918886824944548534041378
5 1 0.000000000000000000000000000000000000000000000000000000000000
5 2 0.000000000000000000000000000000000000000000000000000000000000
5 3 0.410459702520260645318174895920453426088035325902848695210406
5 4 0.482713753678866489204726942976896106809132737721421333413261
6 0 0.0859700504902460302188480225945808401411132615636600222593880
6 1 0.000000000000000000000000000000000000000000000000000000000000
6 2 0.000000000000000000000000000000000000000000000000000000000000
6 3 0.330885963040722183948884057658753173648240154838402033448632
6 4 0.489662957309450192844507011135898201178015478433790097210790
6 5 -0.0731856375070850736789057580558988816340355615025188195854775
7 0 0.120930449125333720660378854927668953958938996999703678812621
7 1 0.000000000000000000000000000000000000000000000000000000000000
7 2 0.000000000000000000000000000000000000000000000000000000000000
7 3 0.000000000000000000000000000000000000000000000000000000000000
7 4 0.260124675758295622809007617838335174368108756484693361887839
7 5 0.0325402621549091330158899334391231259332716675992700000776101
7 6 -0.0595780211817361001560122202563305121444953672762930724538856
8 0 0.110854379580391483508936171010218441909425780168656559807038
8 1 0.000000000000000000000000000000000000000000000000000000000000
8 2 0.000000000000000000000000000000000000000000000000000000000000
8 3 0.000000000000000000000000000000000000000000000000000000000000
8 4 0.000000000000000000000000000000000000000000000000000000000000
8 5 -0.0605761488255005587620924953655516875526344415354339234619466
8 6 0.321763705601778390100898799049878904081404368603077129251110
8 7 0.510485725608063031577759012285123416744672137031752354067590
9 0 0.112054414752879004829715002761802363003717611158172229329393
9 1 0.000000000000000000000000000000000000000000000000000000000000
9 2 0.000000000000000000000000000000000000000000000000000000000000
9 3 0.000000000000000000000000000000000000000000000000000000000000
9 4 0.000000000000000000000000000000000000000000000000000000000000
9 5 -0.144942775902865915672349828340980777181668499748506838876185
9 6 -0.333269719096256706589705211415746871709467423992115497968724
9 7 0.499269229556880061353316843969978567860276816592673201240332
9 8 0.509504608929686104236098690045386253986643232352989602185060
10 0 0.113976783964185986138004186736901163890724752541486831640341
10 1 0.000000000000000000000000000000000000000000000000000000000000
10 2 0.000000000000000000000000000000000000000000000000000000000000
10 3 0.000000000000000000000000000000000000000000000000000000000000
10 4 0.000000000000000000000000000000000000000000000000000000000000
10 5 -0.0768813364203356938586214289120895270821349023390922987406384
10 6 0.239527360324390649107711455271882373019741311201004119339563
10 7 0.397774662368094639047830462488952104564716416343454639902613
10 8 0.0107558956873607455550609147441477450257136782823280838547024
10 9 -0.327769124164018874147061087350233395378262992392394071906457
11 0 0.0798314528280196046351426864486400322758737630423413945356284
11 1 0.000000000000000000000000000000000000000000000000000000000000
11 2 0.000000000000000000000000000000000000000000000000000000000000
11 3 0.000000000000000000000000000000000000000000000000000000000000
11 4 0.000000000000000000000000000000000000000000000000000000000000
11 5 -0.0520329686800603076514949887612959068721311443881683526937298
11 6 -0.0576954146168548881732784355283433509066159287152968723021864
11 7 0.194781915712104164976306262147382871156142921354409364738090
11 8 0.145384923188325069727524825977071194859203467568236523866582
11 9 -0.0782942710351670777553986729725692447252077047239160551335016
11 10 -0.114503299361098912184303164290554670970133218405658122674674
12 0 0.985115610164857280120041500306517278413646677314195559520529
12 1 0.000000000000000000000000000000000000000000000000000000000000
12 2 0.000000000000000000000000000000000000000000000000000000000000
12 3 0.330885963040722183948884057658753173648240154838402033448632
12 4 0.489662957309450192844507011135898201178015478433790097210790
12 5 -1.37896486574843567582112720930751902353904327148559471526397
12 6 -0.861164195027635666673916999665534573351026060987427093314412
12 7 5.78428813637537220022999785486578436006872789689499172601856
12 8 3.28807761985103566890460615937314805477268252903342356581925
12 9 -2.38633905093136384013422325215527866148401465975954104585807
12 10 -3.25479342483643918654589367587788726747711504674780680269911
12 11 -2.16343541686422982353954211300054820889678036420109999154887
13 0 0.895080295771632891049613132336585138148156279241561345991710
13 1 0.000000000000000000000000000000000000000000000000000000000000
13 2 0.197966831227192369068141770510388793370637287463360401555746
13 3 -0.0729547847313632629185146671595558023015011608914382961421311
13 4 0.0000000000000000000000000000000000000000000000000000000000000
13 5 -0.851236239662007619739049371445966793289359722875702227166105
13 6 0.398320112318533301719718614174373643336480918103773904231856
13 7 3.63937263181035606029412920047090044132027387893977804176229
13 8 1.54822877039830322365301663075174564919981736348973496313065
13 9 -2.12221714704053716026062427460427261025318461146260124401561
13 10 -1.58350398545326172713384349625753212757269188934434237975291
13 11 -1.71561608285936264922031819751349098912615880827551992973034
13 12 -0.0244036405750127452135415444412216875465593598370910566069132
14 0 -0.915176561375291440520015019275342154318951387664369720564660
14 1 1.45453440217827322805250021715664459117622483736537873607016
14 2 0.000000000000000000000000000000000000000000000000000000000000
14 3 0.000000000000000000000000000000000000000000000000000000000000
14 4 -0.777333643644968233538931228575302137803351053629547286334469
14 5 0.000000000000000000000000000000000000000000000000000000000000
14 6 -0.0910895662155176069593203555807484200111889091770101799647985
14 7 0.000000000000000000000000000000000000000000000000000000000000
14 8 0.000000000000000000000000000000000000000000000000000000000000
14 9 0.000000000000000000000000000000000000000000000000000000000000
14 10 0.000000000000000000000000000000000000000000000000000000000000
14 11 0.000000000000000000000000000000000000000000000000000000000000
14 12 0.0910895662155176069593203555807484200111889091770101799647985
14 13 0.777333643644968233538931228575302137803351053629547286334469
15 0 0.100000000000000000000000000000000000000000000000000000000000
15 1 0.000000000000000000000000000000000000000000000000000000000000
15 2 -0.157178665799771163367058998273128921867183754126709419409654
15 3 0.000000000000000000000000000000000000000000000000000000000000
15 4 0.000000000000000000000000000000000000000000000000000000000000
15 5 0.000000000000000000000000000000000000000000000000000000000000
15 6 0.000000000000000000000000000000000000000000000000000000000000
15 7 0.000000000000000000000000000000000000000000000000000000000000
15 8 0.000000000000000000000000000000000000000000000000000000000000
15 9 0.000000000000000000000000000000000000000000000000000000000000
15 10 0.000000000000000000000000000000000000000000000000000000000000
15 11 0.000000000000000000000000000000000000000000000000000000000000
15 12 0.000000000000000000000000000000000000000000000000000000000000
15 13 0.000000000000000000000000000000000000000000000000000000000000
15 14 0.157178665799771163367058998273128921867183754126709419409654
16 0 0.181781300700095283888472062582262379650443831463199521664945
16 1 0.675000000000000000000000000000000000000000000000000000000000
16 2 0.342758159847189839942220553413850871742338734703958919937260
16 3 0.000000000000000000000000000000000000000000000000000000000000
16 4 0.259111214548322744512977076191767379267783684543182428778156
16 5 -0.358278966717952089048961276721979397739750634673268802484271
16 6 -1.04594895940883306095050068756409905131588123172378489286080
16 7 0.930327845415626983292300564432428777137601651182965794680397
16 8 1.77950959431708102446142106794824453926275743243327790536000
16 9 0.100000000000000000000000000000000000000000000000000000000000
16 10 -0.282547569539044081612477785222287276408489375976211189952877
16 11 -0.159327350119972549169261984373485859278031542127551931461821
16 12 -0.145515894647001510860991961081084111308650130578626404945571
16 13 -0.259111214548322744512977076191767379267783684543182428778156
16 14 -0.342758159847189839942220553413850871742338734703958919937260
16 15 -0.675000000000000000000000000000000000000000000000000000000000
The estimate of the local truncation error is (1/360) h ( f(t1,x1)-f(t15,x15) )
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