Coefficients of the symplectic splitting method (40,0,1)
with m=40, r = 0 and θ′ = 1
Table 1 of the paper "Error
analysis of splitting methods for the time
dependent
Schrödinger equation", by Sergio Blanes, Fernando Casas, and
Ander
Murua.
a(1)=0.00319482621994375350238999857342677561113145
b(1)=0.00945981882030407477712887370787759811673353
a(2)=0.0153530925375376582164536101788856346974511
b(2)=0.0206416844169440648522660842403851580602606
a(3)=0.0251508890496781281477280947853513060146261
b(3)=0.0288434816591685251884737052023031725183139
a(4)=0.0317972252729596078621719049944247615445730
b(4)=0.0340126222033226715664635927656233127967919
a(5)=0.0357802034934973483171526425171030268963034
b(5)=0.0380171099437430998716337143245852511406177
a(6)=0.0374275006270988541741396306248665873592834
b(6)=0.0339192911286686504679691098693353169712411
a(7)=0.0904596192226880179468474944384663284276355
b(7)=-0.0175902120799474347122094532699023315357414
a(8)=0.00922981837789088195460141269688518557568699
b(8)=0.00998233466328676310954104388699746066438232
a(9)=-0.0560525374924809843787780191224583674138692
b(9)=0.0515947824138131420480583119247744466635734
a(10)=0.0368181614567188680562447398215575135212513
b(10)=0.0371413396409511678325514156103710413088670
a(11)=0.0345703987288785998655299648300209692344651
b(11)=0.0568388614647845906192548349646825248523930
a(12)=-0.0359390690419726244571386385481745705803819
b(12)=-0.00689510642960628564835540029359574230073709
a(13)=0.0807883107538667794330233692202203688932991
b(13)=0.0228440593628484842203597024713275010655035
a(14)=0.0337082872915883302874013901858698729419783
b(14)=0.0466521701065604787092359731409365635636568
a(15)=0.0449538649756733077687385828398617838057206
b(15)=0.0437685394025611637967920971759988473313217
a(16)=0.0450301333821851991569614272726305270252759
b(16)=0.0477302898683470598200291552350652015228114
a(17)=0.0536157142509655725814274855366768476138385
b(17)=0.0943758135232881180448724645383469403481244
a(18)=-0.00717344379245318867880706639973909298739362
b(18)=-0.0286551752567583625854639956681612580074806
a(19)=0.0718005757016858359154100528606720213484694
b(19)=0.0539200984455224571405311246061065099657154
a(20)=0.0532182810267037510580993668756021017569183
b(20)=0.0551117153633706863416084708038920598612203
a(21)=0.0362094643106517152696709161663496984380183
b(21)=0.0141199293078053138060309915522152579190209
a(22)=0.0566713967901626509127230897852103527515108
b(22)=-0.0217164922200657169801301335943455872831531
a(23)=-0.0126701040643029620895280269486472505640533
b(23)=0.0909224659850482798429243986957818942330321
a(24)=0.0600015220685273504165941733322197214847837
b(24)=0.0433808524560821468006755102896239759079954
a(25)=0.0150076731008656655816640807111894633526303
b(25)=0.0421732760950094030442214111104192705940892
a(26)=-0.0355003136179341501872205408521745986445698
b(26)=-0.00689141940062674273448379022300342634783161
a(27)=0.0959686688916670428378438451970947024012207
b(27)=0.0353316442940342341186035786468860482102427
a(28)=0.0275281305788141832064304542296654715306759
b(28)=0.100202561129287790480591742366169965048524
a(29)=-0.00343991823608989854117945351971055610055287
b(29)=-0.0541830197779143256143915559045566488715616
a(30)=0.0401190444625966337418946839848489134563592
b(30)=0.0362365827514375862478734697158183182429277
a(31)=-0.0881861896526550054151637213881412115448346
b(31)=-0.00193814166806146353379441868107177203165230
a(32)=0.117629727030675364607652474698006187860038
b(32)=0.0239006113570048185434266615256445744546543
a(33)=0.0842727902394615519812870708424416049039766
b(33)=0.00672346579182734421049275099740716926831753
a(34)=0.0406059342976000915746091835334649350046831
b(34)=-0.00475138595911251039023831728186214324117224
a(35)=-0.0931292545508556565016806771406296931999442
b(35)=0.0221767577730789928192545764894438160607054
a(36)=-0.0310652740425814140347088481449518934683498
b(36)=-0.00744861057656017267363339375299891352986005
a(37)=0.0499824003071553372684570128057109217323982
b(37)=-0.0902436720810639043632819698659199624028134
a(38)=0.00468798809206868486456831801177608080111117
b(38)=0.0258060750718905974451079925840797671446384
a(39)=-0.00646185623592919727949048035379317519223056
b(39)=0.0870643846494105002858805305538231623772403
a(40)=0.0287700722196174904220708963988898586324443
b(40)=0.0274206163596741687746602737855117578265000
a(41)=0.00926624596846932108539501236684886470431135
b(41)=0.