tobbie247

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7 years, 104 days

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These are questions asked by tobbie247

hello people

I have this computation which has to do with my undergraduate project and each time I compute some work (vary parameters), it seems to evaluate forever. although my computer isn't recent and has 2GB of RAM the computation didn't seem to me as much of a task for it. computation works fine with some parameters as 0 but the moment I change it to a natural number, it evaluates forever.

Is there anyway I could speed up computation in maple? or do I just need a faster computer? but I have a dead line for next week. can I upload my worksheet for someone here to help me execute? 

thank you in advance. 

 

restart; Digits := 10; F[0] := 0; F[1] := 0; F[2] := (1/2)*A; T[0] := 1; T[1] := B; M := 2; S := 1; Pr := 1

for k from 0 to 12 do F[k+3] := (-3*(sum((k+1-r)*(k+2-r)*F[r]*F[k+2-r], r = 0 .. k))+2*(sum((r+1)*F[r+1]*(k+1-r)*F[k+1-r], r = 0 .. k))+M*(k+1)*F[k+1]-T[k])*factorial(k)/factorial(k+3); T[k+2] := (-3*Pr*(sum((k+1-r)*F[r]*T[k+1-r], r = 0 .. k))-S*T[k])*factorial(k)/factorial(k+2) end do:

(1/630)*x^7*A*B+(1/8064)*x^9*A*B-(121/1209600)*x^10*A^2*B+(19/369600)*x^11*A*B-(11/725760)*x^12*A^2*B+(97/19958400)*x^12*A*B^2+(1/12)*x^4*A-(1/24)*x^4*B+(1/120)*x^5*A^2+(1/180)*x^6*A-(1/720)*x^6*B-(1/630)*x^7*A^2-(13/40320)*x^8*A^3+(11/20160)*x^8*A-(11/40320)*x^8*B-(19/60480)*x^9*A^2-(1/45360)*x^9*B^2+(391/3628800)*x^10*A+(37/604800)*x^10*A^3-(23/1814400)*x^10*B-(41/39916800)*x^11*B^2+(229/13305600)*x^11*A^4-(439/7983360)*x^11*A^2+(197/21772800)*x^12*A-(883/159667200)*x^12*B+(29/1520640)*x^12*A^3+(1/2)*A*x^2-(1/6)*x^3-(1/120)*x^5-(1/1680)*x^7-(11/362880)*x^9-(23/2661120)*x^11

(1)

print(expand(t)):

1-(20747/79833600)*x^12*A*B+(29/1680)*x^7*A^2*B-(451/241920)*x^10*A^3*B-(2507/14515200)*x^12*A^3*B+(2921/13305600)*x^11*A*B^2-(33/4480)*x^8*A*B+(761/403200)*x^10*A*B+(1/48)*x^6*A*B-(1/8)*x^4*A*B+(977/887040)*x^11*A^2*B+(1349/4838400)*x^12*A^2*B^2-(1/1152)*x^9*A^2*B-(11/7560)*x^9*A*B^2-(37/44800)*x^10*A^2+(223/604800)*x^10*B^2+(47/633600)*x^11*A-(7913/19958400)*x^11*B+(193/6652800)*x^11*B^3+(1409/1478400)*x^11*A^3-(4813/53222400)*x^12*B^2-(167/221760)*x^12*A^2+(3/40)*x^5*A+(1/30)*x^5*B+(1/240)*x^6*B^2-(1/560)*x^7*A-(23/2520)*x^7*B-(43/4480)*x^8*A^2-(1/896)*x^8*B^2+(61/13440)*x^9*A+(31/22680)*x^9*B-(1/6)*B*x^3+B*x+(2573/95800320)*x^12-(1/2)*x^2+(1/24)*x^4-(13/720)*x^6+(11/8064)*x^8-(2143/3628800)*x^10

(2)

solve({limit(numapprox:-pade(t, x, [2, 2]), x = infinity) = 0., limit(numapprox:-pade(diff(f, x), x, [2, 2]), x = infinity) = 1}, {A, B});

{A = -.7359903327, B = 1.324616408}, {A = -0.7307377025e-1+2.009578912*I, B = .3744177908+.5971332133*I}, {A = .6936483785+.1660915631*I, B = .1622123331+.9257041678*I}, {A = -2.182873922*I, B = .8203849935*I}, {A = .3431199285*I, B = 1.783825109*I}, {A = -.6936483785+.1660915631*I, B = -.1622123331+.9257041678*I}, {A = 0.7307377025e-1+2.009578912*I, B = -.3744177908+.5971332133*I}, {A = .7359903327, B = -1.324616408}, {A = 0.7307377025e-1-2.009578912*I, B = -.3744177908-.5971332133*I}, {A = -.6936483785-.1660915631*I, B = -.1622123331-.9257041678*I}, {A = 2.182873922*I, B = -.8203849935*I}, {A = -.3431199285*I, B = -1.783825109*I}, {A = .6936483785-.1660915631*I, B = .1622123331-.9257041678*I}, {A = -0.7307377025e-1-2.009578912*I, B = .3744177908-.5971332133*I}

(3)

solve({limit(numapprox:-pade(t, x, [3, 3]), x = infinity) = 0., limit(numapprox:-pade(diff(f, x), x, [3, 3]), x = infinity) = 1}, {A, B});

{A = 4.154051132, B = 17.13248053}, {A = .5466914672+.2697341397*I, B = .1291930705+.9494499975*I}, {A = .4506017673+.3824137679*I, B = -.2437153257+1.192091322*I}, {A = .5458260296+.5776530367*I, B = .3085138074+1.260130057*I}, {A = .3007754662+.5799020019*I, B = 0.8347381159e-1+1.033103936*I}, {A = .3916946210+1.036293227*I, B = .9202208108+1.239552889*I}, {A = .1349186305+.5994923360*I, B = 1.926737919+1.099451808*I}, {A = .5141206762+2.582294380*I, B = -.7917198503+.5287783790*I}, {A = 1.669898274*I, B = 1.659206265*I}, {A = 3.170666197*I, B = -.6372670837*I}, {A = -.5141206762+2.582294380*I, B = .7917198503+.5287783790*I}, {A = -.1349186305+.5994923360*I, B = -1.926737919+1.099451808*I}, {A = -.3916946210+1.036293227*I, B = -.9202208108+1.239552889*I}, {A = -.3007754662+.5799020019*I, B = -0.8347381159e-1+1.033103936*I}, {A = -.5458260296+.5776530367*I, B = -.3085138074+1.260130057*I}, {A = -.4506017673+.3824137679*I, B = .2437153257+1.192091322*I}, {A = -.5466914672+.2697341397*I, B = -.1291930705+.9494499975*I}, {A = -4.154051132, B = -17.13248053}, {A = -.5466914672-.2697341397*I, B = -.1291930705-.9494499975*I}, {A = -.4506017673-.3824137679*I, B = .2437153257-1.192091322*I}, {A = -.5458260296-.5776530367*I, B = -.3085138074-1.260130057*I}, {A = -.3007754662-.5799020019*I, B = -0.8347381159e-1-1.033103936*I}, {A = -.3916946210-1.036293227*I, B = -.9202208108-1.239552889*I}, {A = -.1349186305-.5994923360*I, B = -1.926737919-1.099451808*I}, {A = -.5141206762-2.582294380*I, B = .7917198503-.5287783790*I}, {A = -1.669898274*I, B = -1.659206265*I}, {A = -3.170666197*I, B = .6372670837*I}, {A = .5141206762-2.582294380*I, B = -.7917198503-.5287783790*I}, {A = .1349186305-.5994923360*I, B = 1.926737919-1.099451808*I}, {A = .3916946210-1.036293227*I, B = .9202208108-1.239552889*I}, {A = .3007754662-.5799020019*I, B = 0.8347381159e-1-1.033103936*I}, {A = .5458260296-.5776530367*I, B = .3085138074-1.260130057*I}, {A = .4506017673-.3824137679*I, B = -.2437153257-1.192091322*I}, {A = .5466914672-.2697341397*I, B = .1291930705-.9494499975*I}

(4)

 

Download D.T.M.mw

restart:

with(student):

with(plots):

with(plots):

Digits := 19:

inf := 28.5:

equ1 := diff(f(eta), eta, eta, eta)+3*(diff(f(eta), eta, eta))*f(eta)-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+theta(eta) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+3*(diff(diff(f(eta), eta), eta))*f(eta)-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+theta(eta) = 0

(1)

equ2 := diff(theta(eta), eta, eta)+3*Pr*f(eta)*(diff(theta(eta), eta))+S*theta(eta) = 0;

diff(diff(theta(eta), eta), eta)+3*Pr*f(eta)*(diff(theta(eta), eta))+S*theta(eta) = 0

(2)

FNS := f(eta), theta(eta);

f(eta), theta(eta)

(3)

s := 0:

BC := f(0) = s, (D(f))(0) = 0, (D(f))(inf) = 1, theta(0) = 1, theta(inf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(f))(28.5) = 1, theta(0) = 1, theta(28.5) = 0

(4)

CODE := [M = 2, Pr = 1, S = 1]:

S1 := dsolve({BC, subs(CODE, equ1), subs(CODE, equ2)}, {f(eta), theta(eta)}, type = numeric):

S1(0)

[eta = 0., f(eta) = 0., diff(f(eta), eta) = 0., diff(diff(f(eta), eta), eta) = .7424080874401649594, theta(eta) = 1.000000000000000000, diff(theta(eta), eta) = .9438662130843066161]

(5)

NULL

NULL

 

Download shooting_method.mw

Thank you so much for your time. Here's the real problem

f'''(η) + 3f(η)f''(η) - 2[f'(η)] 2 + θ(η) - m*f'(η) = 0

θ''(η) + 3*Pr*f(η)θ'(η) + s*θ(η) = 0

Boundary conditions are:

at η=0: f(η)=f'(η)=0; θ(η)=1;

as η→∞ f'(η)=1; θ(η)=0;

Where m = magnetic parameter (in this case taken as 2)

S = shrinking parameter (in this case taken as 1)

Pr = taken as 1 too

I haven't been able to solve this using differential transforms method (i.e getting the values of f''(0) and θ'(0) denoted by A and B respectively) but shooting method works just fine. :( I seriously need help with this. Thanks you in advance.
I've attached my codes above and i'm hoping someone helps me out real soon. thanks very one.

hello everyone. I have an undergradute project i'm currently working on and I'm stuck where I have to use the Differential Transforms Method to solve a problem with boundary conditions at infinity


restart;

Digits := 5;

F[0] := 0; F[1] := 0; F[2] := (1/2)*A; T[0] := 1; T[1] := B; M := 2; S := 1;

for k from 0 to 10 do F[k+3] := (2*(sum((r+1)*F[r+1]*(k+1-r)*F[k+1-r], r = 0 .. k))-T[k]-3*(sum((k+1-r)*(k+2-r)*F[r]*F[k+2-r], r = 0 .. k))-M*(k+1)*F[k+1])*factorial(k)/factorial(k+3);

T[k+2] := (-3*(sum((k+1-r)*F[r]*T[k+1-r], r = 0 .. k))-S*T[k])*factorial(k)/factorial(k+2)

end do; f := 0; t := 0;

for k from 0 to 10 do

f := f+F[k]*x^k;

t := t+T[k]*x^k end do;

print(f);
print(t);

but the problem is that i cant seem to evaluate

or higer diagonal pade-approximant. any help will be greatly appreciated. thank you.

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