Items tagged with parameter

I hoped that Maple would return the value of 1 in all commands (see below). However, introducing a scaling parameter, sigma, yields the unevaluated expression. Why? I still think it should evaluate to the value of 1.

 

kind regards,

Harry (not a mathematician, but a psychologist)

 

 

 

integral.mw

 

i have attchassignment.mwsassignment.pdf

 

 

hi .how i can clarify expression in maple that in running dont asked me again..

for example attached file

2)how i can deleted one parameter of 
Memory in maple or
Restart it??

hi.i encounter error in pdsole equations with unknown parameter(N)??

please help me for solve it....thanks alotmaple_prime.mw

Dear Maple users

Physical experiment: I dropped a ball with low mass from a height of approximately 7 meters and wanted to test if the air resistance was proportional to the square of the velocity. I filmed the fall and used the program Logger Pro to collect data: a number of datapoints (time,height) was collected. I copy/pasted the datapoints into MS Excel, from where I could import data into Maple via Tools > Assistants > Import Data ... Then I wanted to make a fit with the theoretical solution, given by a function having just one parameter: the Drag coefficient. Unfortunately I received an error "complex values encountered" (see below). I can solve the problem manual by making a number of guesses for the drag coefficient, until the theoretical curve approximates the data points well. I wanted to make Maple do the fitting job, though. I will appreciate if someone could give an idea how to fit the data properly.

NB! Mass m and g is defined above in the Maple document. The Statistics and plots package is called too.

Hello

i have an ODE like this:

I sove this ODE with plot order:

with(plots);
odeplot(sol, [x, (3*D1*a+4*D2)*P(x)/((1-q*S(x))*D2)], .5 .. (1/2)*Pi, tickmarks = [[seq((1/10)*i*Pi = (180*i*(1/10))*`°`, i = 1 .. 8)], default]);
my plot work very well. but i need to plot this ODE with five different parameter (q for for instance, q=0.1 & q=0.2 ....) all in one axis. something like this:

Dear collegues

Hope you are fine

I wrote a code to solve a system of ODEs.

The code solve the problem for higher values of parameter NBT>=5. When I decrease it to NBT=0.2, the code didnt converge. I did my best but I couldnt get the results.

I would be most grateful if you help me at this problem

The code is attached

Thank you

Final_code.mw

 

Amir

Collatz := proc (n)

    local count;

       while n != 1 do

           if `mod`(n, 2) = 0 then n := (1/2)*n

           else n := 3*n+1

           end if;

           count := count+1;

       end do;

print(count);

end proc:

 

I wanna correct 'illegal use of formal parameter' error.

'n' always goes to 1 through 'while statement'.

Bubble := proc (X::list)

local n, i, j, t;

n := nops(X);

if n = 0 then ERROR("empty list") end if;

for i to n-1 do

   for j to n-i do

      if X[j+1] < X[j] then

          t := X[j];

          X[j] := X[j+1];

          X[j+1] := t;

      end if;

   end do;

end do;

print(X);

end proc

 

I make bubble sort algorithm. but i can't find 'illegal use of a formal parameter'.

Hi fellow Maple users,

I'm trying to solve an eigenvalue problem of Ax=wx, where A is a 6 by 6 Hermitian matrix with two parameters x and y. I want to solve it for w and then plot3d it with x and y as unknowns. The way I have been doing is first find the characteristic equation Determinant(A-wI)=0 and then solve it for w, and then plot3d the solutions within a range for x and y. My problem is sometimes solve(Determinant(A-wI)=0,w) would give me the 6 solutions expressed in x and y, but sometimes when the numbers in A are changed it will only give me a Rootof solution with which I cannot plot. I'm wondering if there is a better way to do this. I'm actually not very interested in the symbolic solution of w expressed in x and y, just the plot, so if there is a numerical alternative it's good too.

Thank you in advance!

Hello everybody.

In the attached file, you find 6 equations. All of these parameters are known except "pd" and "qd". How can I find these two unknowns from 6 equations??? It should be pointed out that, "pd" and "qd" must contain "ud", "vd","wd" and "rd".

Thanks in advance.

D.mw

hi.I want to dsolve set of nonlinear equations with one unknown parameter ...is this possible with dsolve rule.in matlab this possible with bvp4c rule..please help me for this problem.if we should another rule please attached file reform.Thanks alot12.mw

 

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.

Hi everyone. Can enuone help with small parameter method?

restart;

eq := diff(x(t), `$`(t, 2))-epsilon(alpha*x(t)^4-beta)*(diff(x(t), t))-x(t)+x(t)^3;

subs(x(t) = 1+epsilon*x[1](t)+epsilon^2*x[2](t), eq);

pls help with this...

Let I  be a polynomial in K[A][X] s.t. A is a sequence of parameters (coefficients of f in F) and X is a sequence of variables. I want to extract the variables from ideal I.

For example if I=[(a-1)x*y^2-b+x, x-y+x^2-c] s.t. a,b,c are parameters and x,y are variables. I want {x,y} as the output of algorithm.

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