This disc contains the files: DEXT22.FOR Double precision version of the package. MEXT22.FOR Quadruple precision version for VAX/VMS. SAMPLE.LOG Output of DEXT22.FOR run under VAX/VMS with the input paramanters set to: Case No. of rules 1 3 Gauss-Legendre 2 3 Gauss-Lobatto 3 3 Gauss-Radau 4 2 Gauss-Laguerre 5 2 Gauss-Hermite 6 3 Gauss-Jacobi Log of output from DEXT22 for: ========================================================= Case No. of rules 1 3 Gauss-Legendre 2 3 Gauss-Lobatto 3 3 Gauss-Radau 4 2 Gauss-Laguerre 5 2 Gauss-Hermite 6 3 Gauss-Jacobi ========================================================= RUN DEXT22 Case ?: 1 No. of rules?: 3 Gauss-Legendre 3-point extension Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00*P( 0,X) 0.0000000000000000D+00*P( 1,X) 0.0000000000000000D+00*P( 2,X) 0.1000000000000000D+01*P( 3,X) New nodes REAL IMAGINARY FLAG ERR 0.0000000000000000D+00 0.0000000000000000D+00 0 0.0D+00 0.7745966692414834D+00 0.0000000000000000D+00 0 0.0D+00 -0.7745966692414834D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.1000000000000000D+01*P( 3,X)/HI Complete extended rule: STEP= 1 POINTS= 3 IFLAG=0 NODES ADDED= 3 No. NODE WEIGHT 1 0.7745966692414834D+00 0.5555555555555555D+00 2 0.0000000000000000D+00 0.8888888888888889D+00 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.9999999999999999D+00 TEST( 2)= 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.1571268237934905D-01*P( 0,X) 0.0000000000000000D+00*P( 1,X) -0.7407407407407407D+00*P( 2,X) 0.0000000000000000D+00*P( 3,X) 0.1000000000000000D+01*P( 4,X) New nodes REAL IMAGINARY FLAG ERR 0.4342437493468026D+00 0.0000000000000000D+00 0 0.0D+00 -0.4342437493468026D+00 0.0000000000000000D+00 0 0.0D+00 0.9604912687080203D+00 0.0000000000000000D+00 0 0.0D+00 -0.9604912687080203D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.0000000000000000D+00*P( 4,X)/HI -0.4444444444444444D+00*P( 5,X)/HI 0.0000000000000000D+00*P( 6,X)/HI 0.1000000000000000D+01*P( 7,X)/HI Complete extended rule: STEP= 2 POINTS= 7 IFLAG=0 NODES ADDED= 4 No. NODE WEIGHT 1 0.9604912687080203D+00 0.1046562260264673D+00 2 0.7745966692414834D+00 0.2684880898683335D+00 3 0.4342437493468026D+00 0.4013974147759622D+00 4 0.0000000000000000D+00 0.4509165386584741D+00 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 TEST( 4)= 0.1000000000000000D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: 0.5772349298067298D-03*P( 0,X) 0.0000000000000000D+00*P( 1,X) 0.1407910917434097D-02*P( 2,X) 0.0000000000000000D+00*P( 3,X) 0.2790650691523971D+00*P( 4,X) 0.0000000000000000D+00*P( 5,X) -0.1205049839843540D+01*P( 6,X) 0.0000000000000000D+00*P( 7,X) 0.1000000000000000D+01*P( 8,X) New nodes REAL IMAGINARY FLAG ERR 0.2233866864289669D+00 0.0000000000000000D+00 0 0.2D-17 -0.2233866864289669D+00 0.0000000000000000D+00 0 0.2D-17 0.6211029467372264D+00 0.0000000000000000D+00 0 0.1D-17 -0.6211029467372264D+00 0.0000000000000000D+00 0 0.1D-17 0.8884592328722570D+00 0.0000000000000000D+00 0 0.3D-17 -0.8884592328722570D+00 0.0000000000000000D+00 0 0.3D-17 0.9938319632127550D+00 0.0000000000000000D+00 0 0.1D-17 -0.9938319632127550D+00 0.0000000000000000D+00 0 0.1D-17 New full extended expansion 0.0000000000000000D+00*P( 8,X)/HI -0.2896464423067150D-01*P( 9,X)/HI 0.0000000000000000D+00*P( 10,X)/HI 0.3461310330856246D+00*P( 11,X)/HI 0.0000000000000000D+00*P( 12,X)/HI -0.1000000000000000D+01*P( 13,X)/HI 0.0000000000000000D+00*P( 14,X)/HI 0.7705426896934803D+00*P( 15,X)/HI Complete extended rule: STEP= 3 POINTS= 15 IFLAG=0 NODES ADDED= 8 No. NODE WEIGHT 1 0.9938319632127550D+00 0.1700171962994028D-01 2 0.9604912687080203D+00 0.5160328299707982D-01 3 0.8884592328722570D+00 0.9292719531512452D-01 4 0.7745966692414834D+00 0.1344152552437843D+00 5 0.6211029467372264D+00 0.1715119091363914D+00 6 0.4342437493468026D+00 0.2006285293769890D+00 7 0.2233866864289669D+00 0.2191568584015875D+00 8 0.0000000000000000D+00 0.2255104997982067D+00 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 TEST( 4)= 0.1000000000000000D+01 Case ?: 2 No. of rules?: 3 Lobatto 2-point extension Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00*P( 0,X) 0.1000000000000000D+01*P( 1,X) New nodes REAL IMAGINARY FLAG ERR 0.0000000000000000D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion -0.1000000000000000D+01*P( 1,X)/HI 0.0000000000000000D+00*P( 2,X)/HI 0.4285714285714286D+00*P( 3,X)/HI Complete extended rule: STEP= 1 POINTS= 3 IFLAG=0 NODES ADDED= 1 No. NODE WEIGHT 1 0.1000000000000000D+01 0.3333333333333333D+00 2 0.0000000000000000D+00 0.1333333333333333D+01 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: -0.1428571428571429D+00*P( 0,X) 0.0000000000000000D+00*P( 1,X) 0.1000000000000000D+01*P( 2,X) New nodes REAL IMAGINARY FLAG ERR 0.6546536707079772D+00 0.0000000000000000D+00 0 0.0D+00 -0.6546536707079771D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.0000000000000000D+00*P( 2,X)/HI -0.1000000000000000D+01*P( 3,X)/HI 0.0000000000000000D+00*P( 4,X)/HI 0.6363636363636364D+00*P( 5,X)/HI Complete extended rule: STEP= 2 POINTS= 5 IFLAG=0 NODES ADDED= 2 No. NODE WEIGHT 1 0.1000000000000000D+01 0.1000000000000000D+00 2 0.6546536707079772D+00 0.5444444444444445D+00 3 0.0000000000000000D+00 0.7111111111111111D+00 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: -0.4746768383132019D-01*P( 0,X) 0.0000000000000000D+00*P( 1,X) -0.1515151515151515D+00*P( 2,X) 0.0000000000000000D+00*P( 3,X) 0.1000000000000000D+01*P( 4,X) New nodes REAL IMAGINARY FLAG ERR 0.3409822659109930D+00 0.0000000000000000D+00 0 0.0D+00 -0.3409822659109930D+00 0.0000000000000000D+00 0 0.0D+00 0.8904055275126688D+00 0.0000000000000000D+00 0 0.2D-17 -0.8904055275126688D+00 0.0000000000000000D+00 0 0.2D-17 New full extended expansion 0.0000000000000000D+00*P( 4,X)/HI -0.3813459268004723D+00*P( 5,X)/HI 0.0000000000000000D+00*P( 6,X)/HI -0.9870129870129869D+00*P( 7,X)/HI 0.0000000000000000D+00*P( 8,X)/HI 0.1000000000000000D+01*P( 9,X)/HI Complete extended rule: STEP= 3 POINTS= 9 IFLAG=0 NODES ADDED= 4 No. NODE WEIGHT 1 0.1000000000000000D+01 0.3064373897707232D-01 2 0.8904055275126688D+00 0.1792626995532074D+00 3 0.6546536707079772D+00 0.2839787780481211D+00 4 0.3409822659109930D+00 0.3342337398164177D+00 5 0.0000000000000000D+00 0.3437620872103631D+00 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 TEST( 4)= 0.1000000000000000D+01 Case ?: 3 No. of rules?: 3 Radau 6-point extension Iteration 1 Coefficients of expansion whose roots are the new nodes: -0.9090909090909092D-01*P( 0,X) 0.2727272727272728D+00*P( 1,X) -0.4545454545454546D+00*P( 2,X) 0.6363636363636364D+00*P( 3,X) -0.8181818181818182D+00*P( 4,X) 0.1000000000000000D+01*P( 5,X) New nodes REAL IMAGINARY FLAG ERR 0.1240503795052277D+00 0.0000000000000000D+00 0 0.4D-17 0.6039731642527837D+00 0.0000000000000000D+00 0 0.6D-17 -0.3909285467072722D+00 0.0000000000000000D+00 0 0.6D-17 0.9203802858970625D+00 0.0000000000000000D+00 0 0.3D-17 -0.8029298284023471D+00 0.0000000000000000D+00 0 0.3D-17 New full extended expansion 0.1000000000000000D+01*P( 5,X)/HI 0.8461538461538462D+00*P( 6,X)/HI Complete extended rule: STEP= 1 POINTS= 6 IFLAG=0 NODES ADDED= 5 No. NODE WEIGHT 1 0.9203802858970625D+00 0.2015883852534808D+00 2 0.6039731642527837D+00 0.4169013343119077D+00 3 0.1240503795052277D+00 0.5209267831895750D+00 4 -0.3909285467072722D+00 0.4853871884689699D+00 5 -0.8029298284023471D+00 0.3196407532205109D+00 6 -0.1000000000000000D+01 0.5555555555555556D-01 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 TEST( 4)= 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.1238920331102971D-01*P( 0,X) -0.1115360783931244D-01*P( 1,X) 0.2930949908491627D-01*P( 2,X) -0.2573880815371107D-01*P( 3,X) -0.8051048473617479D+00*P( 4,X) -0.6245367209597196D+00*P( 5,X) 0.7380888520433050D+00*P( 6,X) 0.1000000000000000D+01*P( 7,X) New nodes REAL IMAGINARY FLAG ERR -0.1366416372713493D+00 0.0000000000000000D+00 0 0.9D-18 -0.6212165636007762D+00 0.0000000000000000D+00 0 0.4D-17 0.3761018966748717D+00 0.0000000000000000D+00 0 0.4D-17 -0.8487727816552522D+00 0.0000000000000000D+00 0 0.4D-17 0.7905296024586544D+00 0.0000000000000000D+00 0 0.4D-17 0.9865012767506534D+00 0.0000000000000000D+00 0 0.2D-17 -0.9439342521493506D+00 0.0000000000000000D+00 0 0.2D-17 New full extended expansion -0.8815438503554517D-01*P( 7,X)/HI -0.8472981649987972D-01*P( 8,X)/HI -0.3768076078707027D+00*P( 9,X)/HI -0.4473580103536859D+00*P( 10,X)/HI 0.3851866566831191D+00*P( 11,X)/HI 0.1000000000000000D+01*P( 12,X)/HI 0.5106460045718307D+00*P( 13,X)/HI Complete extended rule: STEP= 2 POINTS= 13 IFLAG=0 NODES ADDED= 7 No. NODE WEIGHT 1 0.9865012767506534D+00 0.3610633344712083D-01 2 0.9203802858970625D+00 0.9797463317823482D-01 3 0.7905296024586544D+00 0.1603549149394082D+00 4 0.6039731642527837D+00 0.2100921244820766D+00 5 0.3761018966748717D+00 0.2427304474580505D+00 6 0.1240503795052277D+00 0.2588076132975782D+00 7 -0.1366416372713493D+00 0.2601366692626690D+00 8 -0.3909285467072722D+00 0.2455064597946105D+00 9 -0.6212165636007762D+00 0.2115512241336131D+00 10 -0.8029298284023471D+00 0.1329820397038908D+00 11 -0.8487727816552522D+00 0.3616137156650629D-01 12 -0.9439342521493506D+00 0.9202712852123144D-01 13 -0.1000000000000000D+01 0.1556904021500967D-01 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 TEST( 4)= 0.1000000000000000D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: -0.2568241533603606D+00*P( 0,X) 0.6273882318514978D+00*P( 1,X) -0.6950114612492999D+00*P( 2,X) 0.3514310704836285D+00*P( 3,X) 0.2414864785768811D+00*P( 4,X) -0.9310510552284522D+00*P( 5,X) 0.1469801497278645D+01*P( 6,X) -0.5792538945795940D+01*P( 7,X) 0.4360460897303821D+01*P( 8,X) -0.1885604119806995D+02*P( 9,X) 0.1887338563566692D+01*P( 10,X) 0.6992128566633852D+02*P( 11,X) -0.1072921826820173D+02*P( 12,X) -0.4426841333562902D+02*P( 13,X) 0.1000000000000000D+01*P( 14,X) New nodes REAL IMAGINARY FLAG ERR 0.9979162551518678D+00 0.0000000000000000D+00 0 0.1D-16 -0.6134267604635425D-02 0.0000000000000000D+00 0 0.1D-16 0.9613067296650284D+00 0.0000000000000000D+00 0 0.7D-17 -0.2655914229442032D+00 0.0000000000000000D+00 0 0.7D-17 0.8632649380482529D+00 0.0000000000000000D+00 0 0.8D-17 0.7034887989758216D+00 0.0000000000000000D+00 0 0.8D-17 0.4941080138619341D+00 0.0000000000000000D+00 0 0.4D-16 0.2520863057103871D+00 0.0000000000000000D+00 0 0.4D-16 -0.7205766157140713D+00 0.0000000000000000D+00 0 0.2D-16 -0.5103354152259295D+00 0.0000000000000000D+00 0 0.2D-16 -0.9812660421998112D+00 0.0000000000000000D+00 0 0.1D-15 -0.8923964308975302D+00 0.0000000000000000D+00 0 0.1D-15 0.2307179086994016D+02 0.0000000000000000D+00 0 0.6D-16 -0.1013669616811477D+01 0.0000000000000000D+00 0 0.6D-16 New full extended expansion 0.5454360425671037D-02*P( 14,X)/HI 0.1275790889143820D-02*P( 15,X)/HI 0.1362458441982789D-01*P( 16,X)/HI 0.1061409558174235D-01*P( 17,X)/HI -0.7800045804654459D-01*P( 18,X)/HI -0.6147544605704888D-01*P( 19,X)/HI -0.2027665031851448D+00*P( 20,X)/HI -0.2559758659655763D+00*P( 21,X)/HI 0.5447045628625731D+00*P( 22,X)/HI 0.1000000000000000D+01*P( 23,X)/HI 0.5759468453196904D-02*P( 24,X)/HI -0.7380381496936674D+00*P( 25,X)/HI -0.3289096723205376D+00*P( 26,X)/HI 0.7335603893034949D-02*P( 27,X)/HI Complete extended rule: STEP= 3 POINTS= 27 IFLAG=6 NODES ADDED= 14 No. NODE WEIGHT 1 0.2307179086994016D+02 -0.1710833635652233D-16 2 0.9979162551518678D+00 0.5761238214206027D-02 3 0.9865012767506534D+00 0.1781397602627082D-01 4 0.9613067296650284D+00 0.3288145280959046D-01 5 0.9203802858970625D+00 0.4904105110221086D-01 6 0.8632649380482529D+00 0.6509033800352046D-01 7 0.7905296024586544D+00 0.8015752890516894D-01 8 0.7034887989758216D+00 0.9361527599467614D-01 9 0.6039731642527837D+00 0.1050581380411569D+00 10 0.4941080138619341D+00 0.1143012662323623D+00 11 0.3761018966748717D+00 0.1213546454148586D+00 12 0.2520863057103871D+00 0.1263455706105022D+00 13 0.1240503795052277D+00 0.1294155830050473D+00 14 -0.6134267604635425D-02 0.1306510180165526D+00 15 -0.1366416372713493D+00 0.1300525005145075D+00 16 -0.2655914229442032D+00 0.1275061882372417D+00 17 -0.3909285467072722D+00 0.1227817936161397D+00 18 -0.5103354152259295D+00 0.1155996181401652D+00 19 -0.6212165636007762D+00 0.1056775942146705D+00 20 -0.7205766157140713D+00 0.9232499519844784D-01 21 -0.8029298284023471D+00 0.6879140063252571D-01 22 -0.8487727816552522D+00 0.3092904062992692D-01 23 -0.8923964308975302D+00 0.5477880738383480D-01 24 -0.9439342521493506D+00 0.4546365767396098D-01 25 -0.9812660421998112D+00 0.2876294640770191D-01 26 -0.1000000000000000D+01 0.5992084797070105D-02 27 -0.1013669616811477D+01 -0.1477098223165217D-03 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.9999999999999862D+00 TEST( 2)= 0.9999999999727656D+00 TEST( 3)= 0.9999999436798130D+00 TEST( 4)= 0.9998820691687861D+00 Rule test is unsatisfactory Case ?: 4 No. of rules?: 2 Gauss-Laguerre 2-point extension Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00*P( 0,X) 0.0000000000000000D+00*P( 1,X) 0.1000000000000000D+01*P( 2,X) New nodes REAL IMAGINARY FLAG ERR 0.3414213562373095D+01 0.0000000000000000D+00 0 0.0D+00 0.5857864376269049D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.1000000000000000D+01*P( 2,X)/HI Complete extended rule: STEP= 1 POINTS= 2 IFLAG=0 NODES ADDED= 2 No. NODE WEIGHT 1 0.3414213562373095D+01 0.1464466094067262D+00 2 0.5857864376269049D+00 0.8535533905932737D+00 TEST( 0)= 0.9999999999999999D+00 TEST( 1)= 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.6000000000000000D+01*P( 0,X) -0.1500000000000000D+01*P( 1,X) 0.0000000000000000D+00*P( 2,X) 0.1000000000000000D+01*P( 3,X) New nodes REAL IMAGINARY FLAG ERR 0.8396196974011156D+01 0.0000000000000000D+00 0 0.7D-16 0.3019015129944220D+00 -0.1959389276469933D+01 0 0.2D-16 0.3019015129944220D+00 0.1959389276469933D+01 0 0.2D-16 New full extended expansion 0.8125000000000000D+00*P( 3,X)/HI -0.1000000000000000D+01*P( 4,X)/HI 0.4166666666666667D+00*P( 5,X)/HI Complete extended rule: STEP= 2 POINTS= 5 IFLAG=4 NODES ADDED= 3 Terminated prematurely - see IFLAG Case ?: 5 No. of rules?: 2 Gauss-Hermite 3-point extension Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00*P( 0,X) 0.0000000000000000D+00*P( 1,X) 0.0000000000000000D+00*P( 2,X) 0.1000000000000000D+01*P( 3,X) New nodes REAL IMAGINARY FLAG ERR 0.0000000000000000D+00 0.0000000000000000D+00 0 0.0D+00 0.1224744871391589D+01 0.0000000000000000D+00 0 0.0D+00 -0.1224744871391589D+01 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.1000000000000000D+01*P( 3,X)/HI Complete extended rule: STEP= 1 POINTS= 3 IFLAG=0 NODES ADDED= 3 No. NODE WEIGHT 1 0.1224744871391589D+01 0.2954089751509193D+00 2 0.0000000000000000D+00 0.1181635900603677D+01 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: -0.3000000000000000D+01*P( 0,X) 0.0000000000000000D+00*P( 1,X) -0.2000000000000000D+01*P( 2,X) 0.0000000000000000D+00*P( 3,X) 0.1000000000000000D+01*P( 4,X) New nodes REAL IMAGINARY FLAG ERR 0.0000000000000000D+00 -0.4884800789447105D+00 0 0.0D+00 0.0000000000000000D+00 0.4884800789447105D+00 0 0.0D+00 0.2288801605103822D+01 0.0000000000000000D+00 0 0.2D-16 -0.2288801605103822D+01 0.0000000000000000D+00 0 0.2D-16 New full extended expansion 0.0000000000000000D+00*P( 4,X)/HI 0.3809523809523810D+00*P( 5,X)/HI 0.0000000000000000D+00*P( 6,X)/HI 0.1000000000000000D+01*P( 7,X)/HI Complete extended rule: STEP= 2 POINTS= 7 IFLAG=4 NODES ADDED= 4 Terminated prematurely - see IFLAG Case ?: 6 No. of rules?: 3 Gauss-Jacobi 3-point extension Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00*P( 0,X) 0.0000000000000000D+00*P( 1,X) 0.0000000000000000D+00*P( 2,X) 0.1000000000000000D+01*P( 3,X) New nodes REAL IMAGINARY FLAG ERR 0.1647102868965424D+00 0.0000000000000000D+00 0 0.3D-17 0.9008058292716294D+00 0.0000000000000000D+00 0 0.4D-17 0.5498684992164436D+00 0.0000000000000000D+00 0 0.4D-17 New full extended expansion 0.1000000000000000D+01*P( 3,X)/HI Complete extended rule: STEP= 1 POINTS= 3 IFLAG=0 NODES ADDED= 3 No. NODE WEIGHT 1 0.9008058292716294D+00 0.2332816246559149D+00 2 0.5498684992164436D+00 0.3076023676819127D+00 3 0.1647102868965424D+00 0.1257826743288388D+00 TEST( 0)= 0.9999999999999998D+00 TEST( 1)= 0.9999999999999998D+00 TEST( 2)= 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.8302544967323833D-04*P( 0,X) 0.1808212463080860D-03*P( 1,X) -0.6293935530868694D-01*P( 2,X) 0.0000000000000000D+00*P( 3,X) 0.1000000000000000D+01*P( 4,X) New nodes REAL IMAGINARY FLAG ERR 0.3434982475781609D+00 0.0000000000000000D+00 0 0.2D-17 0.4317458752763439D-01 0.0000000000000000D+00 0 0.2D-17 0.9829837529243084D+00 0.0000000000000000D+00 0 0.8D-17 0.7479904707934259D+00 0.0000000000000000D+00 0 0.8D-17 New full extended expansion -0.1000000000000000D+01*P( 4,X)/HI -0.7540286168214371D+00*P( 5,X)/HI -0.9004851826770350D+00*P( 6,X)/HI 0.5021708298937920D+00*P( 7,X)/HI Complete extended rule: STEP= 2 POINTS= 7 IFLAG=0 NODES ADDED= 4 No. NODE WEIGHT 1 0.9829837529243084D+00 0.4509009780887507D-01 2 0.9008058292716294D+00 0.1136674496440606D+00 3 0.7479904707934259D+00 0.1567638583107757D+00 4 0.5498684992164436D+00 0.1546815936593538D+00 5 0.3434982475781609D+00 0.1161056548660293D+00 6 0.1647102868965424D+00 0.6270539664794700D-01 7 0.4317458752763439D-01 0.1765261572962525D-01 TEST( 0)= 0.1000000000000000D+01 TEST( 1)= 0.1000000000000000D+01 TEST( 2)= 0.1000000000000000D+01 TEST( 3)= 0.1000000000000000D+01 TEST( 4)= 0.1000000000000000D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: 0.1246085068908996D-07*P( 0,X) 0.5106502089882409D-07*P( 1,X) 0.1857830431079363D-06*P( 2,X) 0.3154953497851658D-04*P( 3,X) 0.3729410486893128D-03*P( 4,X) 0.6566133154308339D-02*P( 5,X) -0.6845782043616039D-01*P( 6,X) -0.1121555778222753D+00*P( 7,X) 0.1000000000000000D+01*P( 8,X) New nodes REAL IMAGINARY FLAG ERR 0.9522115224106390D-01 0.0000000000000000D+00 0 0.2D-16 0.1092616002586163D-01 0.0000000000000000D+00 0 0.2D-16 0.4453534840434267D+00 0.0000000000000000D+00 0 0.5D-17 0.2486386449037345D+00 0.0000000000000000D+00 0 0.5D-17 0.8321177481736263D+00 0.0000000000000000D+00 0 0.7D-18 0.6523614224614975D+00 0.0000000000000000D+00 0 0.7D-18 0.9973759430379304D+00 0.0000000000000000D+00 0 0.1D-16 0.9513731441472555D+00 0.0000000000000000D+00 0 0.1D-16 New full extended expansion -0.1000000000000000D+01*P( 8,X)/HI -0.7219216410522186D+00*P( 9,X)/HI -0.4137098497966033D+00*P( 10,X)/HI 0.6243456378913302D+00*P( 11,X)/HI 0.2379858019599160D+00*P( 12,X)/HI 0.3071737360122939D+00*P( 13,X)/HI -0.3226631546888718D+00*P( 14,X)/HI 0.5874911786061134D-01*P( 15,X)/HI Complete extended rule: STEP= 3 POINTS= 15 IFLAG=0 NODES ADDED= 8 No. NODE WEIGHT 1 0.9973759430379304D+00 0.7250785857083849D-02 2 0.9829837529243084D+00 0.2225370714572648D-01 3 0.9513731441472555D+00 0.4003272827656301D-01 4 0.9008058292716294D+00 0.5689076367068382D-01 5 0.8321177481736263D+00 0.7021992138795099D-01 6 0.7479904707934259D+00 0.7836602038520848D-01 7 0.6523614224614975D+00 0.8066055699011988D-01 8 0.5498684992164436D+00 0.7734675361301653D-01 9 0.4453534840434267D+00 0.6936411431773201D-01 10 0.3434982475781609D+00 0.5805035560699054D-01 11 0.2486386449037345D+00 0.4488514434457869D-01 12 0.1647102868965424D+00 0.3135360123263908D-01 13 0.9522115224106390D-01 0.1889127817157171D-01 14 0.4317458752763439D-01 0.8826110122443174D-02 15 0.1092616002586163D-01 0.2274825544359364D-02 TEST( 0)= 0.1000000000000001D+01 TEST( 1)= 0.1000000000000004D+01 TEST( 2)= 0.1000000000000006D+01 TEST( 3)= 0.1000000000000009D+01 TEST( 4)= 0.1000000000000013D+01