Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

Hi

On the latest Maple 2022 version, using dsolve with 1st order ODE and Dirac function returns an incorrect solution

dsolve({D(y)(t) + y(t)/tau = Dirac(t)/tau, y(0) = 0})

See attached image. The correct impulse response should be :

y(t) = exp(-t/tau)*Heaviside(t)/tau

The returned solution is 0 for t = 0 and scaled by a 1/2 for t > 0. I never had such an issue with older Maple versions. Is this a bug or am I doing something wrong

Here is the expected solution followed by the Maple solution:

acer helped me out last week with converting strings to dates which was very helpful. However now I stumble on 2 other problems:

- I do not succeed to plot DS6 (time difference versus a numeric value) and to not understand why

- in the cvs data sheet the length of the columns is not equal. The empty cells are automatical filled with "". This prevents me to use numelems as it will also take into consideration the cells filled with "". Is there a way to prevent this

As usual I would like to thank you all, power users, for your patience and help

Test.mw

Hi Everyone; I have plotted two different expressions separately and then shown them in a single graph. From the final display, we can observe that the peak of one expression, A is larger than that of another expression B. Now, the question is, how do I calculate the decrease or increase in the percentage of both curves? This means the peak of expression A is 20%, 8%, or 7% decreases or increases as of expression A.

Help_percentage_inccrease_or_decrease.mw

more explanation, each curve has its maximum point at some value of x, need to calculate that point for each curve. Then, we combined all curves we observed that the peak of each curve is smaller than others, so I am interested to observing that difference in percentage at the maximum value of x.

for reference, I uploading a file of which idea I want to implement for my problem. This is not my problem, but I want to implement it like this.

For_reference.mw

This is most likely a simple question for the power users of this forum, but I do not manage to find a solution. I have date in an Excel file. The first column consists of dates (mm/dd/yyyy) and the second of time (hh:mm). I can easily concatenate both in Maple using cat("9/7/2023", "10:22") but how can I convert the obtained string into a date+time that Maple understands? 

Thank you in advance for your help.

I create a system of equations (with 9 linear equations and 7 variables).
I get 7 equations from the multiplication of a matrix M with a transposed vector of the 7 variables equals the transposed vector of the 7 variables. Other two simple equations are necessary because they are restrictions. Those two equations a re very simple and thave the 7 variable sin it.
To start I have been trying with fsolve but i haven't been able to solve it yet, as I also get the error: "Error, (in fsolve) number of equations, 9, does not match number of variables, 7"
Have you andy idea to solve this problem? Thanks in advance.

Hi all, any one help  me to find the values of constants by using given condition and then how to varify that the goiven condition varify the expression. I have found manually but want to varify through maple.

help.mw

HPM.mw

  • Please help me
  • How do I write Homotopy Perturbation method for a partial differential equation for this question in Maple?

Download HPM.mw

 

Using the SingularValues command with any output type specified causes this error

Error, (in sanity) invalid input: LinearAlgebra:-SingularValues expects value for keyword parameter output to be of type {list(identical(U,S,Vt,list)), identical(U,S,Vt,list)}, but received [U, S, Vt]

Below is a minimal example to trigger the error. Is there something wrong about how I am calling the function?

restart:
with(LinearAlgebra):

sanity := proc()
  local A,U,S,Vt;
  A :=RandomMatrix(3,10);
  U,S,Vt := SingularValues(A, output=['U','S','Vt']);
end proc:

sanity();

Good day all,

please I am new Maple user, i used the same code to solve boundary layer flow. Itried to use the same code in solving nanofluid but the solution is not coverging at some point. But the author i want to compared my results with had solution at those points.

Is there any way i can get solution of this model at this with these values?. Please i need your help. Thank you in advance

secod_code.mw

NULL

restart

with*plots; ode1 := (1+1/bet)*(diff(f(eta), eta, eta, eta))-(diff(f(eta), eta))^2+f(eta)*(diff(f(eta), eta, eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1+1/bet)*(diff(diff(diff(f(eta), eta), eta), eta))-(diff(f(eta), eta))^2+f(eta)*(diff(diff(f(eta), eta), eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1)

ode2 := (diff(theta(eta), eta, eta))*(1+(4*R*(1/3))*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(theta(eta), eta, eta))) = 0

(diff(diff(theta(eta), eta), eta))*(1+(4/3)*R*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(diff(theta(eta), eta), eta))) = 0

(2)

ode3 := diff(phi(eta), eta, eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(theta(eta), eta, eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(phi(eta), eta, eta))) = 0

diff(diff(phi(eta), eta), eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(diff(theta(eta), eta), eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(diff(phi(eta), eta), eta))) = 0

(3)

bcs1 := f(0) = 0, (D(f))(0) = 1+xi*((D^2)(f))(0), (D(f))(6) = 0, theta(6) = 0, phi(0) = 1+`ς`*(D(phi))(0), theta(0) = 1+Zeta*(D(theta))(0), phi(6) = 0

f(0) = 0, (D(f))(0) = 1+xi*(D(f))(0)^2, (D(f))(6) = 0, theta(6) = 0, phi(0) = 1+varsigma*(D(phi))(0), theta(0) = 1+Zeta*(D(theta))(0), phi(6) = 0

(4)

NULL

 

L := [0., .1, .4, 1]

[0., .1, .4, 1]

(5)

 
  

NULL


  for k to 10 do
      sol_All := dsolve
                 ( eval
                   ( {bcs1, ode1, ode2,ode3},
                     [xi= L[k],R=1, CT=0.2, Gr=0.5, Gc=0.5, lambda1=0.2, lambda2=0.2, Pr=0.72, Nb=0.5,  Le=1, dc=0.2, de=0.2, Nt=0.5, Zeta=0.5, varsigma=0.5, M=1.5, bet=1.5]
                   ),
                   [f(eta), theta(eta),phi(eta)],
                   numeric,
                   output = listprocedure
                 );
      Y_sol || k := rhs(sol_All[5]);
      YP_sol || k := -rhs(sol_All[6]);

feta || k := rhs(sol_All[4]);
      fpeta || k := rhs(sol_All[3]);

phieta || k := rhs(sol_All[8]);
      phipeta || k := rhs(sol_All[7])
  end do:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

for k to 10 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do

0., [Y_sol1(0), YP_sol1(0)]

 

.1, [Y_sol2(0), YP_sol2(0)]

 

.4, [Y_sol3(0), YP_sol3(0)]

 

1, [Y_sol4(0), YP_sol4(0)]

 

Error, invalid subscript selector

 

for k to 10 do L[k], [(feta || k)(0)] end do

0., [feta1(0)]

 

.1, [feta2(0)]

 

.4, [feta3(0)]

 

1, [feta4(0)]

 

Error, invalid subscript selector

 

NULL

Error, mismatched or missing bracket/operator

"for k  from 1 to  10 do L[k], ([phieta ||k(0),phipeta||k(0)]); od; "

 

NULL

  plot( [ seq((Y_sol||j)(eta), j = 1..6)],
         eta = 0 .. 6,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((feta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((fpeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, fprime(eta)],
         axes = boxed
      );
plot( [ seq((phipeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phiprime(eta)],
         axes = boxed
      );

plot( [ seq((phieta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phi(eta)],
         axes = boxed
      );

Warning, expecting only range variable eta in expression Y_sol1(eta) to be plotted but found name Y_sol1

 

 

Warning, expecting only range variable eta in expression YP_sol1(eta) to be plotted but found name YP_sol1

 

 

Warning, expecting only range variable eta in expression feta1(eta) to be plotted but found name feta1

 

 

Warning, expecting only range variable eta in expression fpeta1(eta) to be plotted but found name fpeta1

 

 

Warning, expecting only range variable eta in expression phipeta1(eta) to be plotted but found name phipeta1

 

 

Warning, expecting only range variable eta in expression phieta1(eta) to be plotted but found name phieta1

 

 

Why is Maple not calculating 'sqrt' and continuously showing 'Evaluating'?


 

restart

with(LinearAlgebra); with(PDEtools); with(DifferentialGeometry)

with(plots)

with(Physics)

q := (31.00000000*exp(-4.976*t+2.*x)*exp((-2.488+.8336000001*I)*t+(1.+.2*I)*x)-3.000000000*exp(-4.976*t+2.*x)*exp((2.488+.8336000001*I)*t+(-1.+.2*I)*x)+(94.0*I)*exp(I*(.8336*t+.2000*x))*exp(-4.976*t+2.*x))/((11.50000000*I)*exp(-2.488*t+x)+132.44*exp(-4.976*t+2.*x)-(104.5000000*I)*exp(-7.464*t+3.*x)-5.25*exp(-9.952*t+4.*x)+.25)

(31.00000000*exp(-4.976*t+2.*x)*exp((-2.488+.8336000001*I)*t+(1.+.2*I)*x)-3.000000000*exp(-4.976*t+2.*x)*exp((2.488+.8336000001*I)*t+(-1.+.2*I)*x)+(94.0*I)*exp(I*(.8336*t+.2000*x))*exp(-4.976*t+2.*x))/((11.50000000*I)*exp(-2.488*t+x)+132.44*exp(-4.976*t+2.*x)-(104.5000000*I)*exp(-7.464*t+3.*x)-5.25*exp(-9.952*t+4.*x)+.25)

(1)

assume(x::real); assume(t::real)

q1 := simplify(subs({I = -I}, q))

(-(94.*I)*exp(-I*(.8336*t+.2000*x))+31.*exp((-2.488-.8336000001*I)*t+(1.-.2*I)*x)-3.*exp((2.488-.8336000001*I)*t+(-1.-.2*I)*x))*exp(-4.976*t+2.*x)/(-(11.50000000*I)*exp(-2.488*t+x)+132.44*exp(-4.976*t+2.*x)+(104.5000000*I)*exp(-7.464*t+3.*x)-5.25*exp(-9.952*t+4.*x)+.25)

(2)

q2 := simplify(sqrt(q*q1))

NULL

NULL


 

Download q_sqrt.mw

Hi.

When trying to open my document it says:
''There were problems during the loading process, Your worksheet may become incomplete.''

Would you mind helping me?
I saw some scripts on how to fix it, but simply can't solve it myself.

Regards Samuel

Basismat_2_noter.mw

I am slightly confused as I can't apply the seemingly correct function to a sequence. It seems like modp does not like my inverse. But I am not aware of any other way of finding the modular inverse.  

a := i -> (1025 - 2^(10 - 2^i))^(-1) mod (1025 - 2^(10 - 2*2^i));

proc (i) options operator, arrow; `mod`(1/(1025-2^(10-2^i)), 1025-2^(10-2*2^i)) end proc

(1)

a(1);

5

(2)

a(2);

17

(3)

map(i -> i + 1, {seq(1 .. 4)});

{2, 3, 4, 5}

(4)

map(i -> 1/(1025 - 2^(10 - 2^i)) mod (1025 - 2^(10 - 2*2^i)), {seq(1 .. 4)});

Error, invalid input: modp received 65599/64, which is not valid for its 2nd argument, m

 

map(a, {seq(1 .. 4)});

Error, invalid input: modp received 65599/64, which is not valid for its 2nd argument, m

 

NULL

NULL

Download example.mw

Hi, I am completely new to Maple and I keep getting this message:

Error, invalid input: rhs received 19715.18184, which is not valid for its 1st argument, expr

my code is:

sqq:=Vector(n):
for i from 1 by 1 to n do


pom:=eval(sigma[qq],[K=0.5,Fred=0,Phi[a]=0.8,Phi[p]=0.2,camax=300000,Kmin=0.5,co=11230,c11=6120,c12=12710,c21=14.17,c22=6.61,c13=9270,c23=16.16,c14=9270,c24=16.16,g=0.745430443,R=0.00652,H=0.00081,l=2,P=Pload[i],lambda[Q]=lQres1[i], lambda[Z]=lZres1[i]]):

sqq[i]:=rhs(pom):

end do:

I am trying to get a vector sqq solving the equation sigma[qq] using the constants and vectors written there. Can anybody help me please?

how I can plot phi[2] as a contour like attached figure?

tez-1.mw


 

restart

``

beta := 2.5; lambda := 0.1e-1; b := Pi; a := Pi; alpha := 1; y[1] := 1.5; y[2] := 1.5; x[1] := -1; x[2] := 1; Q[1] := 40; Q[2] := 35

2.5

 

0.1e-1

 

Pi

 

Pi

 

1

 

1.5

 

1.5

 

-1

 

1

 

40

 

35

(1)

NULL

NULL

v := (2*n-1)*Pi/(2*b)

n-1/2

(2)

Delta := exp(2*v*a)*(alpha*v+beta)*(1+lambda)-(1-lambda)*(alpha*v-beta)

1.01*exp(2*(n-1/2)*Pi)*(n+2.000000000)-.99*n+2.970000000

(3)

g[22] := ((alpha*v+beta)*((1+lambda)*exp(-v*abs(x-xi))+(-1+lambda)*exp(-v*(x+xi)))*exp(2*v*a)+(alpha*v-beta)*((1+lambda)*exp(-v*(x+xi))+(-1+lambda)*exp(-v*abs(x-xi))))/(2*v*Delta)

g[21] := ((alpha*v+beta)*exp(v*(2*a+xi))+(alpha*v-beta)*exp(-v*xi))*exp(-v*x)/(v*Delta)

NULL

u[2] := int(2*g[21]*Q[1]*Dirac(xi-x[1])*sin(n*Pi*y[1]/b)/b, xi = -a .. 0)+int(2*g[22]*Q[2]*Dirac(xi-x[2])*sin(n*Pi*y[2]/b)/b, xi = 0 .. infinity)

NULL

phi[2] := sum(u[2](x)*sin(v*y), n = 1 .. 30)

NULL

``

plot3d(phi[2], x = 0 .. 5, y = 0 .. b)

 

NULL


 

Download tez-1.mw


 

restart

``

beta := 2.5; lambda := 0.1e-1; b := Pi; a := Pi; alpha := 1; y[1] := 1.5; y[2] := 1.5; x[1] := -1; x[2] := 1; Q[1] := 40; Q[2] := 35

2.5

 

0.1e-1

 

Pi

 

Pi

 

1

 

1.5

 

1.5

 

-1

 

1

 

40

 

35

(1)

NULL

NULL

v := (2*n-1)*Pi/(2*b)

n-1/2

(2)

Delta := exp(2*v*a)*(alpha*v+beta)*(1+lambda)-(1-lambda)*(alpha*v-beta)

1.01*exp(2*(n-1/2)*Pi)*(n+2.000000000)-.99*n+2.970000000

(3)

g[22] := ((alpha*v+beta)*((1+lambda)*exp(-v*abs(x-xi))+(-1+lambda)*exp(-v*(x+xi)))*exp(2*v*a)+(alpha*v-beta)*((1+lambda)*exp(-v*(x+xi))+(-1+lambda)*exp(-v*abs(x-xi))))/(2*v*Delta)

g[21] := ((alpha*v+beta)*exp(v*(2*a+xi))+(alpha*v-beta)*exp(-v*xi))*exp(-v*x)/(v*Delta)

NULL

u[2] := int(2*g[21]*Q[1]*Dirac(xi-x[1])*sin(n*Pi*y[1]/b)/b, xi = -a .. 0)+int(2*g[22]*Q[2]*Dirac(xi-x[2])*sin(n*Pi*y[2]/b)/b, xi = 0 .. infinity)

NULL

phi[2] := sum(u[2](x)*sin(v*y), n = 1 .. 30)

NULL

``

plot3d(phi[2], x = 0 .. 5, y = 0 .. b)

 

NULL


 

Download tez-1.mw

 

 

Hi,

I am working on an optimization problem, where i want to Maximize numerically a function (it is too complex to have a deriviatve) here a pseudo code:

Maximize(f(x,y,z), initialpoint = {x=1,y=1,z=1},iterationlimit = 9999);

Now i have a constraint on (x,y,z) where I want the maximum of another function be smaller than a threshold. Problem is, that the constraints function does not put it the corresponding x,y,z tupel and therefore the maximization regarding f does not come to a solution.

Maximize(f(x,y,z), {Maximize(g(x,y,z,f),{0<f<1})[1]<Thres},initialpoint = {x=1,y=1,z=1},iterationlimit = 9999);

Maybe you guys have an idea how to solve this.

Best

 

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