samen

25 Reputation

4 Badges

1 years, 41 days

MaplePrimes Activity


These are replies submitted by samen

@tomleslie 
 

restart; `ε` := 1.2; k := 2; M := 3

``

MyEqs := NULL; for i while i <= 2^(k-1)*M do t[i] := (i-.5)/(2^(k-1)*M); MyEqs := MyEqs, 9.797958972*a[1][1]+a[1][2]*(151.7893277*t[i]-37.94733192)+9.797958972*a[2][1]+a[2][2]*(151.7893277*t[i]-113.8419958)+(.3*(1.414213562*a[1][0]+a[1][1]*(9.797958972*t[i]-2.449489743)+a[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*a[2][0]+a[2][1]*(9.797958972*t[i]-7.348469229)+a[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)))*(1.414213562*b[1][0]+b[1][1]*(9.797958972*t[i]-2.449489743)+b[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*b[2][0]+b[2][1]*(9.797958972*t[i]-7.348469229)+b[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830))-.2828427124*e[1][0]-.2*e[1][1]*(9.797958972*t[i]-2.449489743)-.2*e[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)-.2828427124*e[2][0]-.2*e[2][1]*(9.797958972*t[i]-7.348469229)-.2*e[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)+.9899494934*a[1][0]+.7*a[1][1]*(9.797958972*t[i]-2.449489743)+.7*a[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+.9899494934*a[2][0]+.7*a[2][1]*(9.797958972*t[i]-7.348469229)+.7*a[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830) = .5; 9.797958972*b[1][1]+b[1][2]*(151.7893277*t[i]-37.94733192)+9.797958972*b[2][1]+b[2][2]*(151.7893277*t[i]-113.8419958)-(.3*(1.414213562*a[1][0]+a[1][1]*(9.797958972*t[i]-2.449489743)+a[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*a[2][0]+a[2][1]*(9.797958972*t[i]-7.348469229)+a[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)))*(1.414213562*b[1][0]+b[1][1]*(9.797958972*t[i]-2.449489743)+b[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*b[2][0]+b[2][1]*(9.797958972*t[i]-7.348469229)+b[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830))+(.3*(1.414213562*b[1][0]+b[1][1]*(9.797958972*t[i]-2.449489743)+b[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*b[2][0]+b[2][1]*(9.797958972*t[i]-7.348469229)+b[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)))*(1.414213562*c[1][0]+c[1][1]*(9.797958972*t[i]-2.449489743)+c[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*c[2][0]+c[2][1]*(9.797958972*t[i]-7.348469229)+c[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830))+1.414213562*b[1][0]+1.0*b[1][1]*(9.797958972*t[i]-2.449489743)+1.0*b[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*b[2][0]+1.0*b[2][1]*(9.797958972*t[i]-7.348469229)+1.0*b[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830) = 0; 9.797958972*c[1][1]+c[1][2]*(151.7893277*t[i]-37.94733192)+9.797958972*c[2][1]+c[2][2]*(151.7893277*t[i]-113.8419958)-(.3*(1.414213562*b[1][0]+b[1][1]*(9.797958972*t[i]-2.449489743)+b[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*b[2][0]+b[2][1]*(9.797958972*t[i]-7.348469229)+b[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)))*(1.414213562*c[1][0]+c[1][1]*(9.797958972*t[i]-2.449489743)+c[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+1.414213562*c[2][0]+c[2][1]*(9.797958972*t[i]-7.348469229)+c[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830))+3.676955261*c[1][0]+2.6*c[1][1]*(9.797958972*t[i]-2.449489743)+2.6*c[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+3.676955261*c[2][0]+2.6*c[2][1]*(9.797958972*t[i]-7.348469229)+2.6*c[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830) = 0; 9.797958972*e[1][1]+e[1][2]*(151.7893277*t[i]-37.94733192)+9.797958972*e[2][1]+e[2][2]*(151.7893277*t[i]-113.8419958)-.5656854248*c[1][0]-.4*c[1][1]*(9.797958972*t[i]-2.449489743)-.4*c[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)-.5656854248*c[2][0]-.4*c[2][1]*(9.797958972*t[i]-7.348469229)-.4*c[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)+2.969848480*e[1][0]+2.1*e[1][1]*(9.797958972*t[i]-2.449489743)+2.1*e[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+2.969848480*e[2][0]+2.1*e[2][1]*(9.797958972*t[i]-7.348469229)+2.1*e[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830) = 0; 9.797958972*g[1][1]+g[1][2]*(151.7893277*t[i]-37.94733192)+9.797958972*g[2][1]+g[2][2]*(151.7893277*t[i]-113.8419958)-1.697056274*e[1][0]-1.2*e[1][1]*(9.797958972*t[i]-2.449489743)-1.2*e[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)-1.697056274*e[2][0]-1.2*e[2][1]*(9.797958972*t[i]-7.348469229)-1.2*e[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830)+.9899494934*g[1][0]+.7*g[1][1]*(9.797958972*t[i]-2.449489743)+.7*g[1][2]*(4.743416490*(4*t[i]-1)^2-1.581138830)+.9899494934*g[2][0]+.7*g[2][1]*(9.797958972*t[i]-7.348469229)+.7*g[2][2]*(4.743416490*(4*t[i]-3)^2-1.581138830) = 0 end do; fsolve([MyEqs])

0.8333333333e-1

 

8.654863759*a[1][1]-24.92928889*a[1][2]+5.225578118*a[2][1]-78.68800918*a[2][2]+.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])-.2828427124*e[1][0]+.3265986324*e[1][1]-.1054092554*e[1][2]-.2828427124*e[2][0]+1.306394530*e[2][1]-6.429964578*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5

 

8.164965810*b[1][1]-24.77117500*b[1][2]+3.265986324*b[2][1]-69.04306231*b[2][2]-.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])+.3*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])*(1.414213562*c[1][0]-1.632993162*c[1][1]+.527046277*c[1][2]+1.414213562*c[2][0]-6.531972648*c[2][1]+32.14982289*c[2][2])+1.414213562*b[1][0]+1.414213562*b[2][0] = 0

 

5.552176751*c[1][1]-23.92790096*c[1][2]-7.185169908*c[2][1]-17.60334569*c[2][2]-.3*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])*(1.414213562*c[1][0]-1.632993162*c[1][1]+.527046277*c[1][2]+1.414213562*c[2][0]-6.531972648*c[2][1]+32.14982289*c[2][2])+3.676955261*c[1][0]+3.676955261*c[2][0] = 0

 

6.368673332*e[1][1]-24.19142410*e[1][2]-3.919183588*e[2][1]-33.67825713*e[2][2]-.5656854248*c[1][0]+.6531972648*c[1][1]-.2108185108*c[1][2]-.5656854248*c[2][0]+2.612789059*c[2][1]-12.85992916*c[2][2]+2.969848480*e[1][0]+2.969848480*e[2][0] = 0

 

8.654863759*g[1][1]-24.92928889*g[1][2]+5.225578118*g[2][1]-78.68800918*g[2][2]-1.697056274*e[1][0]+1.959591794*e[1][1]-.6324555324*e[1][2]-1.697056274*e[2][0]+7.838367178*e[2][1]-38.57978747*e[2][2]+.9899494934*g[1][0]+.9899494934*g[2][0] = 0

 

.2500000000

 

8.654863759*a[1][1]-24.92928889*a[1][2]+5.225578118*a[2][1]-78.68800918*a[2][2]+.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])-.2828427124*e[1][0]+.3265986324*e[1][1]-.1054092554*e[1][2]-.2828427124*e[2][0]+1.306394530*e[2][1]-6.429964578*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 9.797958972*a[1][1]+6.368673332*a[2][1]-63.71989489*a[2][2]+.3*(1.414213562*a[1][0]-1.581138830*a[1][2]+1.414213562*a[2][0]-4.898979486*a[2][1]+17.39252713*a[2][2])*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])-.2828427124*e[1][0]+.3162277660*e[1][2]-.2828427124*e[2][0]+.9797958972*e[2][1]-3.478505426*e[2][2]+.9899494934*a[1][0]-1.106797181*a[1][2]+.9899494934*a[2][0] = .5

 

9.797958972*b[1][1]+4.898979486*b[2][1]-58.50213675*b[2][2]-.3*(1.414213562*a[1][0]-1.581138830*a[1][2]+1.414213562*a[2][0]-4.898979486*a[2][1]+17.39252713*a[2][2])*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])+.3*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])*(1.414213562*c[1][0]-1.581138830*c[1][2]+1.414213562*c[2][0]-4.898979486*c[2][1]+17.39252713*c[2][2])+1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0] = 0

 

9.797958972*c[1][1]-2.939387688*c[2][1]-30.67409334*c[2][2]-.3*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])*(1.414213562*c[1][0]-1.581138830*c[1][2]+1.414213562*c[2][0]-4.898979486*c[2][1]+17.39252713*c[2][2])+3.676955261*c[1][0]-4.110960958*c[1][2]+3.676955261*c[2][0] = 0

 

9.797958972*e[1][1]-.489897948*e[2][1]-39.37035691*e[2][2]-.5656854248*c[1][0]+.6324555320*c[1][2]-.5656854248*c[2][0]+1.959591794*c[2][1]-6.957010852*c[2][2]+2.969848480*e[1][0]-3.320391543*e[1][2]+2.969848480*e[2][0] = 0

 

9.797958972*g[1][1]+6.368673332*g[2][1]-63.71989489*g[2][2]-1.697056274*e[1][0]+1.897366596*e[1][2]-1.697056274*e[2][0]+5.878775383*e[2][1]-20.87103256*e[2][2]+.9899494934*g[1][0]-1.106797181*g[1][2]+.9899494934*g[2][0] = 0

 

.4166666667

 

8.654863759*a[1][1]-24.92928889*a[1][2]+5.225578118*a[2][1]-78.68800918*a[2][2]+.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])-.2828427124*e[1][0]+.3265986324*e[1][1]-.1054092554*e[1][2]-.2828427124*e[2][0]+1.306394530*e[2][1]-6.429964578*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 9.797958972*a[1][1]+6.368673332*a[2][1]-63.71989489*a[2][2]+.3*(1.414213562*a[1][0]-1.581138830*a[1][2]+1.414213562*a[2][0]-4.898979486*a[2][1]+17.39252713*a[2][2])*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])-.2828427124*e[1][0]+.3162277660*e[1][2]-.2828427124*e[2][0]+.9797958972*e[2][1]-3.478505426*e[2][2]+.9899494934*a[1][0]-1.106797181*a[1][2]+.9899494934*a[2][0] = .5, 10.94105418*a[1][1]+25.66715369*a[1][2]+7.511768545*a[2][1]-45.80032148*a[2][2]+.3*(1.414213562*a[1][0]+1.632993162*a[1][1]+.527046279*a[1][2]+1.414213562*a[2][0]-3.265986324*a[2][1]+6.851601593*a[2][2])*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])-.2828427124*e[1][0]-.3265986324*e[1][1]-.1054092558*e[1][2]-.2828427124*e[2][0]+.6531972648*e[2][1]-1.370320319*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5

 

11.43095213*b[1][1]+25.82526757*b[1][2]+6.531972648*b[2][1]-43.74484100*b[2][2]-.3*(1.414213562*a[1][0]+1.632993162*a[1][1]+.527046279*a[1][2]+1.414213562*a[2][0]-3.265986324*a[2][1]+6.851601593*a[2][2])*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])+.3*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])*(1.414213562*c[1][0]+1.632993162*c[1][1]+.527046279*c[1][2]+1.414213562*c[2][0]-3.265986324*c[2][1]+6.851601593*c[2][2])+1.414213562*b[1][0]+1.414213562*b[2][0] = 0

 

14.04374119*c[1][1]+26.66854162*c[1][2]+1.306394530*c[2][1]-32.78227845*c[2][2]-.3*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])*(1.414213562*c[1][0]+1.632993162*c[1][1]+.527046279*c[1][2]+1.414213562*c[2][0]-3.265986324*c[2][1]+6.851601593*c[2][2])+3.676955261*c[1][0]+3.676955261*c[2][0] = 0

 

13.22724461*e[1][1]+26.40501848*e[1][2]+2.939387692*e[2][1]-36.20807924*e[2][2]-.5656854248*c[1][0]-.6531972648*c[1][1]-.2108185116*c[1][2]-.5656854248*c[2][0]+1.306394530*c[2][1]-2.740640637*c[2][2]+2.969848480*e[1][0]+2.969848480*e[2][0] = 0

 

10.94105418*g[1][1]+25.66715369*g[1][2]+7.511768545*g[2][1]-45.80032148*g[2][2]-1.697056274*e[1][0]-1.959591794*e[1][1]-.6324555348*e[1][2]-1.697056274*e[2][0]+3.919183589*e[2][1]-8.221921912*e[2][2]+.9899494934*g[1][0]+.9899494934*g[2][0] = 0

 

.5833333333

 

8.654863759*a[1][1]-24.92928889*a[1][2]+5.225578118*a[2][1]-78.68800918*a[2][2]+.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])-.2828427124*e[1][0]+.3265986324*e[1][1]-.1054092554*e[1][2]-.2828427124*e[2][0]+1.306394530*e[2][1]-6.429964578*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 9.797958972*a[1][1]+6.368673332*a[2][1]-63.71989489*a[2][2]+.3*(1.414213562*a[1][0]-1.581138830*a[1][2]+1.414213562*a[2][0]-4.898979486*a[2][1]+17.39252713*a[2][2])*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])-.2828427124*e[1][0]+.3162277660*e[1][2]-.2828427124*e[2][0]+.9797958972*e[2][1]-3.478505426*e[2][2]+.9899494934*a[1][0]-1.106797181*a[1][2]+.9899494934*a[2][0] = .5, 10.94105418*a[1][1]+25.66715369*a[1][2]+7.511768545*a[2][1]-45.80032148*a[2][2]+.3*(1.414213562*a[1][0]+1.632993162*a[1][1]+.527046279*a[1][2]+1.414213562*a[2][0]-3.265986324*a[2][1]+6.851601593*a[2][2])*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])-.2828427124*e[1][0]-.3265986324*e[1][1]-.1054092558*e[1][2]-.2828427124*e[2][0]+.6531972648*e[2][1]-1.370320319*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 12.08414940*a[1][1]+55.39256368*a[1][2]+8.654863759*a[2][1]-24.92928891*a[2][2]+.3*(1.414213562*a[1][0]+3.265986324*a[1][1]+6.851601593*a[1][2]+1.414213562*a[2][0]-1.632993162*a[2][1]+.527046279*a[2][2])*(1.414213562*b[1][0]+3.265986324*b[1][1]+6.851601593*b[1][2]+1.414213562*b[2][0]-1.632993162*b[2][1]+.527046279*b[2][2])-.2828427124*e[1][0]-.6531972648*e[1][1]-1.370320319*e[1][2]-.2828427124*e[2][0]+.3265986324*e[2][1]-.1054092558*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5

 

13.06394530*b[1][1]+57.44804416*b[1][2]+8.164965810*b[2][1]-24.77117503*b[2][2]-.3*(1.414213562*a[1][0]+3.265986324*a[1][1]+6.851601593*a[1][2]+1.414213562*a[2][0]-1.632993162*a[2][1]+.527046279*a[2][2])*(1.414213562*b[1][0]+3.265986324*b[1][1]+6.851601593*b[1][2]+1.414213562*b[2][0]-1.632993162*b[2][1]+.527046279*b[2][2])+.3*(1.414213562*b[1][0]+3.265986324*b[1][1]+6.851601593*b[1][2]+1.414213562*b[2][0]-1.632993162*b[2][1]+.527046279*b[2][2])*(1.414213562*c[1][0]+3.265986324*c[1][1]+6.851601593*c[1][2]+1.414213562*c[2][0]-1.632993162*c[2][1]+.527046279*c[2][2])+1.414213562*b[1][0]+1.414213562*b[2][0] = 0

 

18.28952341*c[1][1]+68.41060671*c[1][2]+5.552176751*c[2][1]-23.92790098*c[2][2]-.3*(1.414213562*b[1][0]+3.265986324*b[1][1]+6.851601593*b[1][2]+1.414213562*b[2][0]-1.632993162*b[2][1]+.527046279*b[2][2])*(1.414213562*c[1][0]+3.265986324*c[1][1]+6.851601593*c[1][2]+1.414213562*c[2][0]-1.632993162*c[2][1]+.527046279*c[2][2])+3.676955261*c[1][0]+3.676955261*c[2][0] = 0

 

16.65653025*e[1][1]+64.98480592*e[1][2]+6.368673332*e[2][1]-24.19142412*e[2][2]-.5656854248*c[1][0]-1.306394530*c[1][1]-2.740640637*c[1][2]-.5656854248*c[2][0]+.6531972648*c[2][1]-.2108185116*c[2][2]+2.969848480*e[1][0]+2.969848480*e[2][0] = 0

 

12.08414940*g[1][1]+55.39256368*g[1][2]+8.654863759*g[2][1]-24.92928891*g[2][2]-1.697056274*e[1][0]-3.919183589*e[1][1]-8.221921912*e[1][2]-1.697056274*e[2][0]+1.959591794*e[2][1]-.6324555348*e[2][2]+.9899494934*g[1][0]+.9899494934*g[2][0] = 0

 

.7500000000

 

8.654863759*a[1][1]-24.92928889*a[1][2]+5.225578118*a[2][1]-78.68800918*a[2][2]+.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])-.2828427124*e[1][0]+.3265986324*e[1][1]-.1054092554*e[1][2]-.2828427124*e[2][0]+1.306394530*e[2][1]-6.429964578*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 9.797958972*a[1][1]+6.368673332*a[2][1]-63.71989489*a[2][2]+.3*(1.414213562*a[1][0]-1.581138830*a[1][2]+1.414213562*a[2][0]-4.898979486*a[2][1]+17.39252713*a[2][2])*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])-.2828427124*e[1][0]+.3162277660*e[1][2]-.2828427124*e[2][0]+.9797958972*e[2][1]-3.478505426*e[2][2]+.9899494934*a[1][0]-1.106797181*a[1][2]+.9899494934*a[2][0] = .5, 10.94105418*a[1][1]+25.66715369*a[1][2]+7.511768545*a[2][1]-45.80032148*a[2][2]+.3*(1.414213562*a[1][0]+1.632993162*a[1][1]+.527046279*a[1][2]+1.414213562*a[2][0]-3.265986324*a[2][1]+6.851601593*a[2][2])*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])-.2828427124*e[1][0]-.3265986324*e[1][1]-.1054092558*e[1][2]-.2828427124*e[2][0]+.6531972648*e[2][1]-1.370320319*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 12.08414940*a[1][1]+55.39256368*a[1][2]+8.654863759*a[2][1]-24.92928891*a[2][2]+.3*(1.414213562*a[1][0]+3.265986324*a[1][1]+6.851601593*a[1][2]+1.414213562*a[2][0]-1.632993162*a[2][1]+.527046279*a[2][2])*(1.414213562*b[1][0]+3.265986324*b[1][1]+6.851601593*b[1][2]+1.414213562*b[2][0]-1.632993162*b[2][1]+.527046279*b[2][2])-.2828427124*e[1][0]-.6531972648*e[1][1]-1.370320319*e[1][2]-.2828427124*e[2][0]+.3265986324*e[2][1]-.1054092558*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 13.22724461*a[1][1]+88.06943287*a[1][2]+9.797958972*a[2][1]+.3*(1.414213562*a[1][0]+4.898979486*a[1][1]+17.39252713*a[1][2]+1.414213562*a[2][0]-1.581138830*a[2][2])*(1.414213562*b[1][0]+4.898979486*b[1][1]+17.39252713*b[1][2]+1.414213562*b[2][0]-1.581138830*b[2][2])-.2828427124*e[1][0]-.9797958972*e[1][1]-3.478505426*e[1][2]-.2828427124*e[2][0]+.3162277660*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0]-1.106797181*a[2][2] = .5

 

14.69693846*b[1][1]+93.28719101*b[1][2]+9.797958972*b[2][1]-.3*(1.414213562*a[1][0]+4.898979486*a[1][1]+17.39252713*a[1][2]+1.414213562*a[2][0]-1.581138830*a[2][2])*(1.414213562*b[1][0]+4.898979486*b[1][1]+17.39252713*b[1][2]+1.414213562*b[2][0]-1.581138830*b[2][2])+.3*(1.414213562*b[1][0]+4.898979486*b[1][1]+17.39252713*b[1][2]+1.414213562*b[2][0]-1.581138830*b[2][2])*(1.414213562*c[1][0]+4.898979486*c[1][1]+17.39252713*c[1][2]+1.414213562*c[2][0]-1.581138830*c[2][2])+1.414213562*b[1][0]+1.414213562*b[2][0]-1.581138830*b[2][2] = 0

 

22.53530563*c[1][1]+121.1152344*c[1][2]+9.797958972*c[2][1]-.3*(1.414213562*b[1][0]+4.898979486*b[1][1]+17.39252713*b[1][2]+1.414213562*b[2][0]-1.581138830*b[2][2])*(1.414213562*c[1][0]+4.898979486*c[1][1]+17.39252713*c[1][2]+1.414213562*c[2][0]-1.581138830*c[2][2])+3.676955261*c[1][0]+3.676955261*c[2][0]-4.110960958*c[2][2] = 0

 

20.08581589*e[1][1]+112.4189708*e[1][2]+9.797958972*e[2][1]-.5656854248*c[1][0]-1.959591794*c[1][1]-6.957010852*c[1][2]-.5656854248*c[2][0]+.6324555320*c[2][2]+2.969848480*e[1][0]+2.969848480*e[2][0]-3.320391543*e[2][2] = 0

 

13.22724461*g[1][1]+88.06943287*g[1][2]+9.797958972*g[2][1]-1.697056274*e[1][0]-5.878775383*e[1][1]-20.87103256*e[1][2]-1.697056274*e[2][0]+1.897366596*e[2][2]+.9899494934*g[1][0]+.9899494934*g[2][0]-1.106797181*g[2][2] = 0

 

.9166666667

 

8.654863759*a[1][1]-24.92928889*a[1][2]+5.225578118*a[2][1]-78.68800918*a[2][2]+.3*(1.414213562*a[1][0]-1.632993162*a[1][1]+.527046277*a[1][2]+1.414213562*a[2][0]-6.531972648*a[2][1]+32.14982289*a[2][2])*(1.414213562*b[1][0]-1.632993162*b[1][1]+.527046277*b[1][2]+1.414213562*b[2][0]-6.531972648*b[2][1]+32.14982289*b[2][2])-.2828427124*e[1][0]+.3265986324*e[1][1]-.1054092554*e[1][2]-.2828427124*e[2][0]+1.306394530*e[2][1]-6.429964578*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 9.797958972*a[1][1]+6.368673332*a[2][1]-63.71989489*a[2][2]+.3*(1.414213562*a[1][0]-1.581138830*a[1][2]+1.414213562*a[2][0]-4.898979486*a[2][1]+17.39252713*a[2][2])*(1.414213562*b[1][0]-1.581138830*b[1][2]+1.414213562*b[2][0]-4.898979486*b[2][1]+17.39252713*b[2][2])-.2828427124*e[1][0]+.3162277660*e[1][2]-.2828427124*e[2][0]+.9797958972*e[2][1]-3.478505426*e[2][2]+.9899494934*a[1][0]-1.106797181*a[1][2]+.9899494934*a[2][0] = .5, 10.94105418*a[1][1]+25.66715369*a[1][2]+7.511768545*a[2][1]-45.80032148*a[2][2]+.3*(1.414213562*a[1][0]+1.632993162*a[1][1]+.527046279*a[1][2]+1.414213562*a[2][0]-3.265986324*a[2][1]+6.851601593*a[2][2])*(1.414213562*b[1][0]+1.632993162*b[1][1]+.527046279*b[1][2]+1.414213562*b[2][0]-3.265986324*b[2][1]+6.851601593*b[2][2])-.2828427124*e[1][0]-.3265986324*e[1][1]-.1054092558*e[1][2]-.2828427124*e[2][0]+.6531972648*e[2][1]-1.370320319*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 12.08414940*a[1][1]+55.39256368*a[1][2]+8.654863759*a[2][1]-24.92928891*a[2][2]+.3*(1.414213562*a[1][0]+3.265986324*a[1][1]+6.851601593*a[1][2]+1.414213562*a[2][0]-1.632993162*a[2][1]+.527046279*a[2][2])*(1.414213562*b[1][0]+3.265986324*b[1][1]+6.851601593*b[1][2]+1.414213562*b[2][0]-1.632993162*b[2][1]+.527046279*b[2][2])-.2828427124*e[1][0]-.6531972648*e[1][1]-1.370320319*e[1][2]-.2828427124*e[2][0]+.3265986324*e[2][1]-.1054092558*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5, 13.22724461*a[1][1]+88.06943287*a[1][2]+9.797958972*a[2][1]+.3*(1.414213562*a[1][0]+4.898979486*a[1][1]+17.39252713*a[1][2]+1.414213562*a[2][0]-1.581138830*a[2][2])*(1.414213562*b[1][0]+4.898979486*b[1][1]+17.39252713*b[1][2]+1.414213562*b[2][0]-1.581138830*b[2][2])-.2828427124*e[1][0]-.9797958972*e[1][1]-3.478505426*e[1][2]-.2828427124*e[2][0]+.3162277660*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0]-1.106797181*a[2][2] = .5, 14.37033983*a[1][1]+123.6977612*a[1][2]+10.94105418*a[2][1]+25.66715370*a[2][2]+.3*(1.414213562*a[1][0]+6.531972648*a[1][1]+32.14982289*a[1][2]+1.414213562*a[2][0]+1.632993162*a[2][1]+.527046279*a[2][2])*(1.414213562*b[1][0]+6.531972648*b[1][1]+32.14982289*b[1][2]+1.414213562*b[2][0]+1.632993162*b[2][1]+.527046279*b[2][2])-.2828427124*e[1][0]-1.306394530*e[1][1]-6.429964578*e[1][2]-.2828427124*e[2][0]-.3265986324*e[2][1]-.1054092558*e[2][2]+.9899494934*a[1][0]+.9899494934*a[2][0] = .5

 

16.32993162*b[1][1]+133.3427081*b[1][2]+11.43095213*b[2][1]+25.82526758*b[2][2]-.3*(1.414213562*a[1][0]+6.531972648*a[1][1]+32.14982289*a[1][2]+1.414213562*a[2][0]+1.632993162*a[2][1]+.527046279*a[2][2])*(1.414213562*b[1][0]+6.531972648*b[1][1]+32.14982289*b[1][2]+1.414213562*b[2][0]+1.632993162*b[2][1]+.527046279*b[2][2])+.3*(1.414213562*b[1][0]+6.531972648*b[1][1]+32.14982289*b[1][2]+1.414213562*b[2][0]+1.632993162*b[2][1]+.527046279*b[2][2])*(1.414213562*c[1][0]+6.531972648*c[1][1]+32.14982289*c[1][2]+1.414213562*c[2][0]+1.632993162*c[2][1]+.527046279*c[2][2])+1.414213562*b[1][0]+1.414213562*b[2][0] = 0

 

26.78108785*c[1][1]+184.7824247*c[1][2]+14.04374119*c[2][1]+26.66854162*c[2][2]-.3*(1.414213562*b[1][0]+6.531972648*b[1][1]+32.14982289*b[1][2]+1.414213562*b[2][0]+1.632993162*b[2][1]+.527046279*b[2][2])*(1.414213562*c[1][0]+6.531972648*c[1][1]+32.14982289*c[1][2]+1.414213562*c[2][0]+1.632993162*c[2][1]+.527046279*c[2][2])+3.676955261*c[1][0]+3.676955261*c[2][0] = 0

 

23.51510153*e[1][1]+168.7075133*e[1][2]+13.22724461*e[2][1]+26.40501849*e[2][2]-.5656854248*c[1][0]-2.612789059*c[1][1]-12.85992916*c[1][2]-.5656854248*c[2][0]-.6531972648*c[2][1]-.2108185116*c[2][2]+2.969848480*e[1][0]+2.969848480*e[2][0] = 0

 

14.37033983*g[1][1]+123.6977612*g[1][2]+10.94105418*g[2][1]+25.66715370*g[2][2]-1.697056274*e[1][0]-7.838367178*e[1][1]-38.57978747*e[1][2]-1.697056274*e[2][0]-1.959591794*e[2][1]-.6324555348*e[2][2]+.9899494934*g[1][0]+.9899494934*g[2][0] = 0

 

Error, (in fsolve) number of equations, 6, does not match number of variables, 18

 

NULL


 

Download solEqs33.mw

@tomleslie thankyou! This Post is so helpful to me, really really helpful

@tomleslie  i want the command parrallel to solve equations...

system picks all equations automaiically after loop.



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/model.mw .
 

Download model.mw

@tomleslie No. fiifteen equatiions fifteen unknowns.. 
 

@acer if i change functtion 
yfunc := proc (t) options operator, arrow; sqrt(202650*t*K/(phi*mu)) end proc

then how to write in form of matrix ??
 

Mfunc := Matrix(10, 10, proc (i, j) options operator, arrow; yfunc(a+(1/9)*(i-1)*(b-a)) end proc)

 

same like this or  somthing change ??? i can't understand how u write this form 

explain please... i shall be very thankful to you 

@acer explain please.  i need ur help.. thank u :)

@acer  thank you.. ur code is very helpfull for me.. 
can you expalin how you write Mfunc??? 
Mfunc := Matrix(10, 10, proc (i, j) options operator, arrow; yfunc(a+(1/9)*(i-1)*(b-a)) end proc)

thank you for your help :)

 

@acer without equ[i,j] or seq cammond how to get the u[i,j] values and write in form of matrix?? Crank_scheme.mwCrank_scheme.mw
ans anminate with change in time k from 0.001..0.33?? 
and difference between function y plot...

@acer  
i want to find the difference between numerical values and experimental values...  for numerical values, discitization scheme use. my discritization scheme is this
 

-lemda*u[i-1,j+1]+(2+2*lemda)*u[i,j+1]-lemda*u[i+1,j+1]=lemda*u[i-1,j]+(2-2*lemda)
*u[i,j]+lemda*u[i+1,j]

estimate the value of u[i,j]  then write in form of matrix to get matrix plot.. i dont know is there an other way to get plot of u[i,j] and next i want to find chnage in time (k) koi k=0.0001 to 0.001... chnage in numerical values with change in time k... 
and i change the data values into function y (time and position ) data..... and plot in 3d to find the difference.. here  explain what i want... 
hope u understard what i want to do.. is there another way to plot discritized scheme then plz do favour.. 
your work error plot is not helpful for me....  plz suggest some other way to understand...... without equ[i,j] or [seq] can i find thevalue of u[i,j] and plot graph simply and find difernce .. minor error ?? 
hope you understand what i want... so plz see n check more what we do to simplify code ?? and get minnor difference

@acer please answer..!! how to fin difference between matrix plot and function plot??? 

@acer plz do one more help .. how to find the differnce between 2 graphs . i want to estimate error. i m a little bit confuse how to minus matrix plot into functioon plot ??? 
 

 


 

restart; Digits := 15; with(plots); with(LinearAlgebra)

NULL

a := 0; b := 1; N := 9; h := (b-a)/(N+1); phi := .5; K := 10^(-6); mu := 1.67; alpha := K/(phi*mu); lambda := alpha*k/h^2

0.119760479041916e-3*k

(1)

NULL

for i from 0 while i <= N do u[i, 0] := h*i+1 end do

NULL

for j from 0 while j <= N+1 do u[0, j] := .1; u[N+1, j] := .5 end do

NULL

printlevel := 2; for i while i <= N do for j from 0 while j <= N do eq[i, j] := lambda*u[i-1, j]+(2-2*lambda)*u[i, j]+lambda*u[i+1, j] = -lambda*u[i-1, j+1]+(2+2*lambda)*u[i, j+1]-lambda*u[i+1, j+1] end do end do; for i while i <= N do for j from 0 while j <= N do eq[i, j] := lambda*u[i-1, j]+(2-2*lambda)*u[i, j]+lambda*u[i+1, j] = -lambda*u[i-1, j+1]+(2+2*lambda)*u[i, j+1]-lambda*u[i+1, j+1] end do end do

NULL

NULL

sys := ([seq])(seq(eq[i, j], j = 0 .. N), i = 1 .. N):

nops(sys);

vars:=indets(sys) minus {k}:

nn := Matrix(N+1, N+1,(i, j)-> u[i-1, j-1]):

##

p:=proc(kk) local u_res,A;

  u_res:=solve(eval(sys,k=kk),vars);

  A:=eval(nn,u_res);

  #plots:-matrixplot(A)

end proc:

90

(2)

## Testing p for k=0.001:

plots:-matrixplot(p(0.0001)-p(0.0009));

 

 

restart; with(plots)

y(t) := 40.049*t+.2456;

40.049*t+.2456

(3)

smartplot3d[y(t), t](40.049*t+.2456)

 

"Error:="

Error, invalid assignment

"Error:="

 

 

``


 

Download error_plot.mw

@acer for N= 49 my system take 24 hours  and no results show... can u help me for geting  results plz 


 

restart; Digits := 15; with(plots); with(LinearAlgebra)

NULL

a := 0; b := 1; N := 19; h := (b-a)/(N+1); phi := .5; K := 10^(-6); mu := 1.67; alpha := K/(phi*mu); lambda := alpha*k/h^2

0.119760479041916e-3*k

(1)

NULL

for i from 0 while i <= N do u[i, 0] := h*i+1 end do

NULL

for j from 0 while j <= N+1 do u[0, j] := .1; u[N+1, j] := .5 end do

NULL

printlevel := 2; for i while i <= N do for j from 0 while j <= N do eq[i, j] := lambda*u[i-1, j]+(2-2*lambda)*u[i, j]+lambda*u[i+1, j] = -lambda*u[i-1, j+1]+(2+2*lambda)*u[i, j+1]-lambda*u[i+1, j+1] end do end do; for i while i <= N do for j from 0 while j <= N do eq[i, j] := lambda*u[i-1, j]+(2-2*lambda)*u[i, j]+lambda*u[i+1, j] = -lambda*u[i-1, j+1]+(2+2*lambda)*u[i, j+1]-lambda*u[i+1, j+1] end do end do

sys := ([seq])(seq(eq[i, j], j = 0 .. N), i = 1 .. N):

nops(sys);

vars:=indets(sys) minus {k}:

nn := Matrix(N+1, N+1,(i, j)-> u[i-1, j-1]):

##

p:=proc(kk) local u_res,A;

  u_res:=solve(eval(sys,k=kk),vars);

  A:=eval(nn,u_res);

  #plots:-matrixplot(A)

end proc:

90

(2)

## Testing p for k=0.001:

plots:-matrixplot(p(0.001)-p(0.0005));

## Animating the plot for k=0.0001..0.001:

plots:-animate(K->plots:-matrixplot(p(k)-p(K)),[k],k=0.0001..0.001);

``


 

Download crnk.mw

 

@Carl Love can we plot this graph in 2d..??? 


 

() .. Nonlinear*Fractional*KdV*equation

() .. Nonlinear*Fractional*KdV*equation

(1)

PDE1 := D[t]^alpha*u(x, t)-3*(u^2)[x]+u[xxx] = 0;

D[t]^alpha*u(x, t)-3*(u^2)[x]+u[xxx] = 0

(2)

u(x, 0) = 6*x, 0 < alpha and alpha <= 1, t > 0:

"Solution : u(x,t)=6*x+(6^(3)*x*t^(alpha))/(GAMMA(alpha+1))+(2*6^(5)*x*t^(2 *alpha))/(GAMMA(2*alpha+1))+((4*6^(7)*x)/(GAMMA(3*alpha+1))+6^(7)*x*(GAMMA(2*alpha+1))/(GAMMA(2*alpha+1)*GAMMA(3*alpha+1)))*t^(3 alpha)+..:"

Error, invalid sum/difference

"Solution : u(x,t)=6*x+(6^3*x*t^alpha)/(GAMMA(alpha+1))+(2*6^5*x*t^(2 *alpha))/(GAMMA(2*alpha+1))+((4*6^7*x)/(GAMMA(3*alpha+1))+6^7*x*(GAMMA(2*alpha+1))/(GAMMA(2*alpha+1)*GAMMA(3*alpha+1)))*t^(3 alpha)+..:"

 

NULL

2.*linear*time*fractional*diffusion*equation

2.*linear*time*fractional*diffusion*equation

(3)

NULL

PDE2 := diff(u(x, t), [`$`(t, alpha)]) = diff(u(x, t), x, x)

diff(u(x, t), [`$`(t, alpha)]) = diff(diff(u(x, t), x), x)

(4)

"IC:= u(x,0):=sinx , 0<alpha<=1 , t>0"

Error, unable to parse

"IC:= u(x,0):=sinx , 0<alpha<=1 , t>0"

 

"Solution : u(x,t)=sinx*(1-(t^(alpha))/(GAMMA(alpha+1))+(t^(2*alpha))/(GAMMA(2 *alpha+1))-(t^(3*alpha))/(GAMMA(3* alpha+1))+(t^(4* alpha))/(GAMMA(4* alpha+1))+..):"

Error, invalid sum/difference

"Solution : u(x,t)=sinx*(1-(t^alpha)/(GAMMA(alpha+1))+(t^(2*alpha))/(GAMMA(2 *alpha+1))-(t^(3*alpha))/(GAMMA(3* alpha+1))+(t^(4* alpha))/(GAMMA(4* alpha+1))+..):"

 


 

Download kdv.mw

@Mariusz Iwaniuk 

1 2 Page 1 of 2