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CodeTools[Profile] --Can't get it to work...

Asked by: Traruh Synred 55
codetools
October 01 2023
0  4

I'm trying to use CodeTools[Profile] to investigate my memory leak and the effect or lack there of of 'forget' to improve it.

I copied my code from an example:

with(CodeTools[Profiling]);
 [Allow, Build, Coverage, GetProfileTable, Ignore, IsProfiled, 

   LoadProfiles, Merge, PrintProfiles, Profile, Remove, 

   SaveProfiles, Select, SortBy, UnProfile]

Profile([PickAngles(1.0, 1.0, 1.0)]);
Error, (in CodeTools:-Profiling:-Profile) unexpected argument(s)

The 'unexpected argument' is the 'result' from 'PickAngles'. I've tried with and w/o the '[]' but it does the same thing failing to recognize that 'PickAngles' is a procedure.

The example I used is here:

https://www.maplesoft.com/support/help/maple/view.aspx?path=CodeTools%2FProfiling%2FProfile procedure.

I did what to make of the subscript Profiles in the example so I used '[Profiles]' and that worked or seemed to.

Why doesn't Maple debugger start for me?...

Asked by: Traruh Synred 55
syntax worksheet debugger
September 22 2023
0  2

When I hit the debug button the debugger does not start. Putting Debug() in the code doesn't either. Is there some initiation I'm missing? It seems to me it used to work.

How do I plot binned data in Maple?...

Asked by: Traruh Synred 55
histogram plotting statistics
September 15 2023
0  6

I have data that I've binned in list. I'd like to plot in as a histogram. 

dataplot sort of does it but doesn't give the x-axis that I used but just the bins.

Yes, I know about Histogram from Statistics. To plot 1000000 values I have to enter them all into a list which seems crazy when all I want is a 100 bin histogram. Doing the binning is trivial, but I can't figure out how to plot it with a sensible x-axis (show range used to define the 'histogram')

Nothing works after updating from Maple 2015 to 20...

Asked by: leouam 25
installation incomplete-question
September 15 2023
0  3

Hello,

I am experiencing difficulties using my old Maple programs with the newer version. I tried changing the types of inputs and the typesetting level, but it just doesn't work. I would appreciate it if someone could help me overcome my ignorance.

Some simple input is attached with the output.

Bin contents in a Histogram?...

Asked by: Traruh Synred 55
histogram statistics
September 14 2023
0  3

How do I find the contents of a bin in a Maple histogram?

Numerical Results from NLPSolve...

Asked by: Traruh Synred 55
eval substitution nlpsolve
September 12 2023
1  4

I'm using NLPSolve to minimize a complicated function. It works great, but the answers are not returned in numerical form which I need as they are then input for the next stage of my program.

How to I extract numbers?

S2 := NLPSolve(test, phi1 = 0 .. 2*Pi, phi2 = 1.0*Pi .. 2*Pi);
     S2 := [-1.00000000011810774, 

       [phi1 = 0.773215730257661, phi2 = 5.98741001513872]]
==>The Result is a list and the solutions appear kind of string-like. 

S2[2,1] returns 'phi=0.773...' not the number I need

time dependent 2d plot...

Asked by: SHIVAS 35
homework pde numeric
September 12 2023
0  5
> 

restart:
> 

  ra:=2: b1:=1.41: na:=0.7: we:=0.5: eta[1]:=4*0.1: d:=0.5:
  xi:=0.1: m:=na: ea:=0.5: pr:=21: gr:=0.1: R:=0.9323556933:
> 

  PDE1:=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(R^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));
  IBC:= {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0};

2*(diff(f(x, t), t)) = 1.41+.705*cos(t)+1.150367877*(diff(diff(f(x, t), x), x))+1.150367877*(diff(f(x, t), x))/x

  

{f(1, t) = 0, f(x, 0) = 0, (D[1](f))(0, t) = 0}

 (1)
> 

sol := pdsolve({PDE1}, IBC, numeric); sol:-plot(f(x, t), t = 1.2, linestyle = "solid", title = "Velocity Profile", labels = ["r", "f"])

 

``

Download pde.mw

for different time plot of f(x,t) in single plot with different color 

1 dependent and 2 independent variables....

Asked by: SHIVAS 35
syntax homework pde
September 06 2023
0  12

modifed_practice.mw

Impact of Shape-Dependent Hybrid Nanofluid on Transient Efficiency of a Fully W
et Porous Longitudinal Fin

dear sir please help me to solve the graph i given reference pdf also. i have implimented the code but getting error in ploting 

Thank you

how to input complex function in a complex differe...

Asked by: bashar27 55
August 20 2023
0  0

restart;
alias(u = u(x, y, t), f = f(x, y, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*t);
                    /     (1/2)\           
                    \f + R     / exp(I R t)
pde1 := I*(diff(u, t))+diff(u, x, x)+2*lambda*u*abs(u)*abs(u)-gamma*(diff(u, x, t));
   // d   \                /     (1/2)\             \
 I ||--- f| exp(I R t) + I \f + R     / R exp(I R t)|
   \\ dt  /                                         /

      / d  / d   \\           
    + |--- |--- f|| exp(I R t)
      \ dx \ dx  //           

               /     (1/2)\                           2 
    + 2 lambda \f + R     / exp(I R t) (exp(-Im(R t)))  

               2
   |     (1/2)| 
   |f + R     | 

            // d  / d   \\                / d   \             \
    - gamma ||--- |--- f|| exp(I R t) + I |--- f| R exp(I R t)|
            \\ dx \ dt  //                \ dx  /             /
 

      

DTM method with Dsolve method comparision...

Asked by: SHIVAS 35
ode homework dsolve
August 18 2023
0  0

how to plot graphs for both methods and comparison of different method values for Diff(f(eta),eta, eta) at eta =0

 

> 

NULL
> 

NULL
> 

restart
> 

F[0] := al
> 

F[1] := a2
> 

F[2] := a3
> 

F[3] := a4
> 

G[0] := a5
> 

G[1] := a6
> 

T[0] := a7
> 

T[1] := a8
> 

Q[0] := a9
> 

Q[1] := a10
> 

n[1] := 1
> 

for k from 0 to n[1] do F[k+4] := solve((1+a)*(k+1)*(k+2)*(k+3)*(k+4)*F[k+4]-a*(k+1)*(k+2)*G[k+2]-R*(sum(F[k-m]*(m+1)*(m+2)*(m+3)*F[m+3], m = 0 .. k))+R*(sum((k-m+1)*F[k-m+1]*(m+1)*(m+2)*F[m+2], m = 0 .. k)), F[k+4]) end do

-(1/12)*(R*a2*a3-3*R*a4*al-a*G[2])/(1+a)

  

-(1/60)*(R^2*a2*a3*al-3*R^2*a4*al^2+2*R*a*a3^2-R*a*al*G[2]+2*R*a3^2-3*a^2*G[3]-3*a*G[3])/(1+a)^2

 (1)
> 

n[2] := 3
> 

for k from 0 to n[2] do G[k+2] := solve(b*(k+1)*(k+2)*G[k+2]+a*(k+1)*(k+2)*F[k+2]-2*a*G[k]-c*R*(sum((m+1)*G[m+1]*F[k-m], m = 0 .. k))+c*R*(sum(G[k-m]*(m+1)*F[m+1], m = 0 .. k)), G[k+2]) end do

-(1/2)*(R*a2*a5*c-R*a6*al*c+2*a*a3-2*a*a5)/b

  

-(1/6)*(R^2*a2*a5*al*c^2-R^2*a6*al^2*c^2+2*R*a*a3*al*c-2*R*a*a5*al*c+2*R*a3*a5*b*c+6*a*a4*b-2*a*a6*b)/b^2

  

-(1/24)*(R^3*a*a2*a5*al^2*c^3-R^3*a*a6*al^3*c^3+R^3*a2*a5*al^2*c^3-R^3*a6*al^3*c^3+2*R^2*a^2*a3*al^2*c^2-2*R^2*a^2*a5*al^2*c^2+R^2*a*a2^2*a5*b*c^2-R^2*a*a2*a6*al*b*c^2+2*R^2*a*a3*a5*al*b*c^2+2*R^2*a*a3*al^2*c^2-2*R^2*a*a5*al^2*c^2+R^2*a2^2*a5*b*c^2-R^2*a2*a6*al*b*c^2+2*R^2*a3*a5*al*b*c^2+2*R*a^2*a2*a3*b*c-R*a^2*a2*a5*b*c+6*R*a^2*a4*al*b*c-3*R*a^2*a6*al*b*c+2*R*a*a3*a6*b^2*c+6*R*a*a4*a5*b^2*c-2*R*a*a2*a3*b^2+2*R*a*a2*a3*b*c+6*R*a*a4*al*b^2+6*R*a*a4*al*b*c-4*R*a*a6*al*b*c+2*R*a3*a6*b^2*c+6*R*a4*a5*b^2*c+2*a^3*a3*b-2*a^3*a5*b+4*a^2*a3*b-4*a^2*a5*b)/(b^3*(1+a))

  

-(1/120)*(R^4*a^2*a2*a5*al^3*c^4-R^4*a^2*a6*al^4*c^4+2*R^4*a*a2*a5*al^3*c^4-2*R^4*a*a6*al^4*c^4+R^4*a2*a5*al^3*c^4-R^4*a6*al^4*c^4+2*R^3*a^3*a3*al^3*c^3-2*R^3*a^3*a5*al^3*c^3+3*R^3*a^2*a2^2*a5*al*b*c^3-3*R^3*a^2*a2*a6*al^2*b*c^3+2*R^3*a^2*a3*a5*al^2*b*c^3+4*R^3*a^2*a3*al^3*c^3-4*R^3*a^2*a5*al^3*c^3+6*R^3*a*a2^2*a5*al*b*c^3-6*R^3*a*a2*a6*al^2*b*c^3+4*R^3*a*a3*a5*al^2*b*c^3+2*R^3*a*a3*al^3*c^3-2*R^3*a*a5*al^3*c^3+3*R^3*a2^2*a5*al*b*c^3-3*R^3*a2*a6*al^2*b*c^3+2*R^3*a3*a5*al^2*b*c^3+6*R^2*a^3*a2*a3*al*b*c^2-4*R^2*a^3*a2*a5*al*b*c^2+6*R^2*a^3*a4*al^2*b*c^2-4*R^2*a^3*a6*al^2*b*c^2+4*R^2*a^2*a2*a3*a5*b^2*c^2-R^2*a^2*a2*a5^2*b^2*c^2+2*R^2*a^2*a3*a6*al*b^2*c^2+6*R^2*a^2*a4*a5*al*b^2*c^2+R^2*a^2*a5*a6*al*b^2*c^2-2*R^2*a^2*a2*a3*al*b^2*c+12*R^2*a^2*a2*a3*al*b*c^2-R^2*a^2*a2*a5*al*b^2*c-6*R^2*a^2*a2*a5*al*b*c^2+6*R^2*a^2*a4*al^2*b^2*c+12*R^2*a^2*a4*al^2*b*c^2+R^2*a^2*a6*al^2*b^2*c-10*R^2*a^2*a6*al^2*b*c^2-2*R^2*a*a2*a3*a5*b^3*c+8*R^2*a*a2*a3*a5*b^2*c^2-R^2*a*a2*a5^2*b^2*c^2+4*R^2*a*a3*a6*al*b^2*c^2+6*R^2*a*a4*a5*al*b^3*c+12*R^2*a*a4*a5*al*b^2*c^2+R^2*a*a5*a6*al*b^2*c^2-2*R^2*a*a2*a3*al*b^3-2*R^2*a*a2*a3*al*b^2*c+6*R^2*a*a2*a3*al*b*c^2-2*R^2*a*a2*a5*al*b*c^2+6*R^2*a*a4*al^2*b^3+6*R^2*a*a4*al^2*b^2*c+6*R^2*a*a4*al^2*b*c^2-6*R^2*a*a6*al^2*b*c^2-2*R^2*a2*a3*a5*b^3*c+4*R^2*a2*a3*a5*b^2*c^2+2*R^2*a3*a6*al*b^2*c^2+6*R^2*a4*a5*al*b^3*c+6*R^2*a4*a5*al*b^2*c^2+4*R*a^4*a3*al*b*c-4*R*a^4*a5*al*b*c+12*R*a^3*a2*a4*b^2*c-4*R*a^3*a2*a6*b^2*c+2*R*a^3*a5^2*b^2*c+12*R*a^2*a4*a6*b^3*c-2*R*a^3*a3*al*b^2+12*R*a^3*a3*al*b*c+2*R*a^3*a5*al*b^2-12*R*a^3*a5*al*b*c+24*R*a^2*a2*a4*b^2*c-8*R*a^2*a2*a6*b^2*c-4*R*a^2*a3^2*b^3+4*R*a^2*a3*a5*b^2*c+2*R*a^2*a5^2*b^2*c+24*R*a*a4*a6*b^3*c+8*R*a^2*a3*al*b*c-8*R*a^2*a5*al*b*c+12*R*a*a2*a4*b^2*c-4*R*a*a2*a6*b^2*c-4*R*a*a3^2*b^3+4*R*a*a3*a5*b^2*c+12*R*a4*a6*b^3*c+6*a^4*a4*b^2-2*a^4*a6*b^2+18*a^3*a4*b^2-6*a^3*a6*b^2+12*a^2*a4*b^2-4*a^2*a6*b^2)/(b^4*(1+a)^2)

 (2)
> 

n[3] := 3
> 

for k from 0 to n[3] do T[k+2] := solve((k+1)*(k+2)*T[k+2]+p3*(k+1)*(k+2)*Q[k+2]+p1*(sum((m+1)*F[m+1]*T[k-m], m = 0 .. k))-p1*(sum(F[k-m]*(m+1)*T[m+1], m = 0 .. k)), T[k+2]) end do

-(1/2)*p1*a2*a7+(1/2)*p1*al*a8-p3*Q[2]

  

-(1/6)*a2*a7*al*p1^2+(1/6)*a8*al^2*p1^2-(1/3)*al*p1*p3*Q[2]-(1/3)*a3*a7*p1-p3*Q[3]

  

-p3*Q[4]-(1/24)*p1^2*a2^2*a7+(1/24)*a2*p1^2*al*a8-(1/12)*p1*a2*p3*Q[2]-(1/12)*p1*a3*a8-(1/4)*p1*a4*a7-(1/24)*a2*a7*al^2*p1^3+(1/24)*a8*al^3*p1^3-(1/12)*al^2*p1^2*p3*Q[2]-(1/12)*al*a3*a7*p1^2-(1/4)*p1*al*p3*Q[3]

  

(1/120)*(-a*a2*a7*al^3*b*p1^4+a*a8*al^4*b*p1^4-2*a*al^3*b*p1^3*p3*Q[2]-a2*a7*al^3*b*p1^4+a8*al^4*b*p1^4-3*a*a2^2*a7*al*b*p1^3+3*a*a2*a8*al^2*b*p1^3-2*a*a3*a7*al^2*b*p1^3-2*al^3*b*p1^3*p3*Q[2]-6*a*a2*al*b*p1^2*p3*Q[2]-6*a*al^2*b*p1^2*p3*Q[3]-3*a2^2*a7*al*b*p1^3+3*a2*a8*al^2*b*p1^3-2*a3*a7*al^2*b*p1^3+R*a*a2*a5*a7*c*p1-R*a*a6*a7*al*c*p1-4*a*a2*a3*a7*b*p1^2-2*a*a3*a8*al*b*p1^2-6*a*a4*a7*al*b*p1^2-6*a2*al*b*p1^2*p3*Q[2]-6*al^2*b*p1^2*p3*Q[3]+2*R*a2*a3*a7*b*p1-6*R*a4*a7*al*b*p1-12*a*a2*b*p1*p3*Q[3]-24*a*al*b*p1*p3*Q[4]-4*a2*a3*a7*b*p1^2-2*a3*a8*al*b*p1^2-6*a4*a7*al*b*p1^2+2*a^2*a3*a7*p1-2*a^2*a5*a7*p1-12*a*a4*a8*b*p1-12*a2*b*p1*p3*Q[3]-24*al*b*p1*p3*Q[4]-120*a*b*p3*Q[5]-12*a4*a8*b*p1-120*b*p3*Q[5])/(b*(1+a))

 (3)
> 

n[4] := 3
> 

for k from 0 to n[4] do Q[k+2] := solve((k+1)*(k+2)*Q[k+2]+p4*(k+1)*(k+2)*Q[k+2]+p2*(sum((m+1)*F[m+1]*Q[k-m], m = 0 .. k))-p2*(sum(F[k-m]*(m+1)*Q[m+1], m = 0 .. k)), Q[k+2]) end do

(1/2)*p2*(a10*al-a2*a9)/(p4+1)

  

(1/6)*p2*(a10*al^2*p2-a2*a9*al*p2-2*a3*a9*p4-2*a3*a9)/(p4+1)^2

  

(1/24)*p2*(a10*al^3*p2^2-a2*a9*al^2*p2^2+a10*a2*al*p2*p4-a2^2*a9*p2*p4-2*a3*a9*al*p2*p4+a10*a2*al*p2-2*a10*a3*p4^2-a2^2*a9*p2-2*a3*a9*al*p2-6*a4*a9*p4^2-4*a10*a3*p4-12*a4*a9*p4-2*a10*a3-6*a4*a9)/(p4+1)^3

  

(1/120)*p2*(a*a10*al^4*b*p2^3-a*a2*a9*al^3*b*p2^3+R*a*a2*a5*a9*c*p4^3-R*a*a6*a9*al*c*p4^3+3*a*a10*a2*al^2*b*p2^2*p4-3*a*a2^2*a9*al*b*p2^2*p4-2*a*a3*a9*al^2*b*p2^2*p4+a10*al^4*b*p2^3-a2*a9*al^3*b*p2^3+3*R*a*a2*a5*a9*c*p4^2-3*R*a*a6*a9*al*c*p4^2+2*R*a2*a3*a9*b*p4^3-6*R*a4*a9*al*b*p4^3+3*a*a10*a2*al^2*b*p2^2-2*a*a10*a3*al*b*p2*p4^2-3*a*a2^2*a9*al*b*p2^2-4*a*a2*a3*a9*b*p2*p4^2-2*a*a3*a9*al^2*b*p2^2-6*a*a4*a9*al*b*p2*p4^2+3*a10*a2*al^2*b*p2^2*p4-3*a2^2*a9*al*b*p2^2*p4-2*a3*a9*al^2*b*p2^2*p4+3*R*a*a2*a5*a9*c*p4-3*R*a*a6*a9*al*c*p4+6*R*a2*a3*a9*b*p4^2-18*R*a4*a9*al*b*p4^2+2*a^2*a3*a9*p4^3-2*a^2*a5*a9*p4^3-4*a*a10*a3*al*b*p2*p4-12*a*a10*a4*b*p4^3-8*a*a2*a3*a9*b*p2*p4-12*a*a4*a9*al*b*p2*p4+3*a10*a2*al^2*b*p2^2-2*a10*a3*al*b*p2*p4^2-3*a2^2*a9*al*b*p2^2-4*a2*a3*a9*b*p2*p4^2-2*a3*a9*al^2*b*p2^2-6*a4*a9*al*b*p2*p4^2+R*a*a2*a5*a9*c-R*a*a6*a9*al*c+6*R*a2*a3*a9*b*p4-18*R*a4*a9*al*b*p4+6*a^2*a3*a9*p4^2-6*a^2*a5*a9*p4^2-2*a*a10*a3*al*b*p2-36*a*a10*a4*b*p4^2-4*a*a2*a3*a9*b*p2-6*a*a4*a9*al*b*p2-4*a10*a3*al*b*p2*p4-12*a10*a4*b*p4^3-8*a2*a3*a9*b*p2*p4-12*a4*a9*al*b*p2*p4+2*R*a2*a3*a9*b-6*R*a4*a9*al*b+6*a^2*a3*a9*p4-6*a^2*a5*a9*p4-36*a*a10*a4*b*p4-2*a10*a3*al*b*p2-36*a10*a4*b*p4^2-4*a2*a3*a9*b*p2-6*a4*a9*al*b*p2+2*a^2*a3*a9-2*a^2*a5*a9-12*a*a10*a4*b-36*a10*a4*b*p4-12*a10*a4*b)/((p4+1)^4*b*(1+a))

 (4)
> 

U[1] := sum(F[r]*t^r, r = 0 .. n[1]+4)
> 

p[1] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[1])
> 

U[2] := sum(G[r]*t^r, r = 0 .. n[2]+2)
> 

p[2] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[2])
> 

U[3] := sum(T[r]*t^r, r = 0 .. n[2]+2)
> 

p[3] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[3])
> 

U[4] := sum(Q[r]*t^r, r = 0 .. n[2]+2)
> 

p[4] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[4])
> 

e1 := subs(t = -1, p[1]) = 0
> 

e2 := subs(t = -1, diff(p[1], t)) = 0
> 

e3 := subs(t = 1, diff(p[1], t)) = -1
> 

e4 := subs(t = 1, p[1]) = 0
> 

e5 := subs(t = -1, p[2]) = 0
> 

e6 := subs(t = 1, p[2]) = 1
> 

e7 := subs(t = -1, p[3]) = 1
> 

e8 := subs(t = 1, p[3]) = 0
> 

e9 := subs(t = -1, p[4]) = 1
> 

e10 := subs(t = 1, p[4]) = 0
> 

j := {e1, e10, e2, e3, e4, e5, e6, e7, e8, e9}
> 

j := solve(j)
> 

sj := evalf(j)

{a10 = -3.476623407, a2 = -5.754056209, a3 = .1776219452, a4 = 11.75811242, a5 = 1.324264301, a6 = -684.5523526, a7 = -.2700369914, a8 = 1.152227714, a9 = 2.191204245, al = 0.3618902741e-1}, {a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916}, {a10 = -4.849411034, a2 = 11.61910224, a3 = -20.01600142, a4 = -22.98820448, a5 = -303.7401922, a6 = -153.4446663, a7 = -7.896832028, a8 = -4.917031955, a9 = -9.645684059, al = 10.13300071}, {a10 = -12.41434918+6.055636678*I, a2 = -6.912869603-3.362489448*I, a3 = -9.364948739-.7062944755*I, a4 = 14.07573921+6.724978896*I, a5 = -106.6284397-3.087774395*I, a6 = 184.4202683+38.56644530*I, a7 = 2.689687372-4.048821750*I, a8 = -4.715343127+5.167588829*I, a9 = 8.474095612-5.785653488*I, al = 4.807474369+.3531472377*I}, {a10 = -8.462156658-37.78952093*I, a2 = -22.10322629+.7748996783*I, a3 = -2.926063539-87.71943544*I, a4 = 44.45645258-1.549799357*I, a5 = 126.1645842+1357.517358*I, a6 = -880.5344239+73.01362458*I, a7 = -96.56841781+19.40514883*I, a8 = -11.30265439-58.49348719*I, a9 = -59.25678527+13.86225901*I, al = 1.588031769+43.85971772*I}, {a10 = 21.28781597+0.9115942334e-2*I, a2 = -2.190767380-.1297694199*I, a3 = 0.4834062985e-1-8.617807139*I, a4 = 4.631534761+.2595388398*I, a5 = -1.070222696-4.103740084*I, a6 = 28.93315819+1.060309794*I, a7 = -.6440073083+2.959900705*I, a8 = 3.178056838-1.712994921*I, a9 = -1.124006374+8.865509135*I, al = .1008296851+4.308903570*I}, {a10 = -2.226772562-4.893664011*I, a2 = -5.213384606-.4953312060*I, a3 = 1.881656676-24.64377975*I, a4 = 10.67676921+.9906624121*I, a5 = -5.922885277-14.38776520*I, a6 = 9.281006594-6.268746147*I, a7 = -8.563253672+2.519226454*I, a8 = -2.293245547-7.112743663*I, a9 = -4.948019289+2.035858706*I, al = -.8158283379+12.32188987*I}, {a10 = -3.311080211+1.380948844*I, a2 = -6.825505968+3.517539795*I, a3 = 10.11566715-.6387142267*I, a4 = 13.90101194-7.035079589*I, a5 = 106.6696011-4.144959139*I, a6 = 183.4179274-43.03852019*I, a7 = -1.117431335-0.4722817327e-1*I, a8 = -1.705921790+.2164542338*I, a9 = -2.431505210+.6185873236*I, al = -4.932833576+.3193571133*I}, {a10 = 1.720689325, a2 = 11.30494181, a3 = 20.89441402, a4 = -22.35988362, a5 = 304.5741226, a6 = -141.0519632, a7 = -3.607319024, a8 = 2.107261122, a9 = -3.764007990, al = -10.32220701}, {a10 = -3.311080211-1.380948844*I, a2 = -6.825505968-3.517539795*I, a3 = 10.11566715+.6387142267*I, a4 = 13.90101194+7.035079589*I, a5 = 106.6696011+4.144959139*I, a6 = 183.4179274+43.03852019*I, a7 = -1.117431335+0.4722817327e-1*I, a8 = -1.705921790-.2164542338*I, a9 = -2.431505210-.6185873236*I, al = -4.932833576-.3193571133*I}, {a10 = -2.226772562+4.893664011*I, a2 = -5.213384606+.4953312060*I, a3 = 1.881656676+24.64377975*I, a4 = 10.67676921-.9906624121*I, a5 = -5.922885277+14.38776520*I, a6 = 9.281006594+6.268746147*I, a7 = -8.563253672-2.519226454*I, a8 = -2.293245547+7.112743663*I, a9 = -4.948019289-2.035858706*I, al = -.8158283379-12.32188987*I}, {a10 = 21.28781597-0.9115942334e-2*I, a2 = -2.190767380+.1297694199*I, a3 = 0.4834062985e-1+8.617807139*I, a4 = 4.631534761-.2595388398*I, a5 = -1.070222696+4.103740084*I, a6 = 28.93315819-1.060309794*I, a7 = -.6440073083-2.959900705*I, a8 = 3.178056838+1.712994921*I, a9 = -1.124006374-8.865509135*I, al = .1008296851-4.308903570*I}, {a10 = -8.462156658+37.78952093*I, a2 = -22.10322629-.7748996783*I, a3 = -2.926063539+87.71943544*I, a4 = 44.45645258+1.549799357*I, a5 = 126.1645842-1357.517358*I, a6 = -880.5344239-73.01362458*I, a7 = -96.56841781-19.40514883*I, a8 = -11.30265439+58.49348719*I, a9 = -59.25678527-13.86225901*I, al = 1.588031769-43.85971772*I}, {a10 = -12.41434918-6.055636678*I, a2 = -6.912869603+3.362489448*I, a3 = -9.364948739+.7062944755*I, a4 = 14.07573921-6.724978896*I, a5 = -106.6284397+3.087774395*I, a6 = 184.4202683-38.56644530*I, a7 = 2.689687372+4.048821750*I, a8 = -4.715343127-5.167588829*I, a9 = 8.474095612+5.785653488*I, al = 4.807474369-.3531472377*I}

 (5)
> 

p[1] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[1])

.2586309916+.2575353882*t-.2672619833*t^2-.2650707765*t^3+0.8630991633e-2*t^4+0.7535388242e-2*t^5

 (6)
> 

p[2] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[2])

0.7065354871e-1+.1172581545*t+.3439809338*t^2+.3401058738*t^3+0.8536551748e-1*t^4+0.4263597162e-1*t^5

 (7)
> 

p[3] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[3])

.6100817436-.5277387253*t-.1364241818*t^2+0.3945483872e-1*t^3+0.2634243820e-1*t^4-0.1171611337e-1*t^5

 (8)
> 

p[4] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[4])

.5842364534-.5218741555*t-.1037943244*t^2+0.3134539737e-1*t^3+0.1955787096e-1*t^4-0.9471241840e-2*t^5

 (9)
> 

NULL
> 

value*of*D@@2*F(0)*For*R = 1, 1.5, `and`(2*Using*Both*DTM*scheme, dsolve*method)
> 

 

Download DTM_practice.mw

How to substitute in argument of the exponential f...

Asked by: sunit 105
substitution exp subsindets
August 15 2023
0  4

Hi,

It might be really trivial, but I am struggling in the algebraic manipulation of the argument of the exponential function. As an example, I want to substitute 

I*T[0]*(omega1-2*omega2) = I*omega2*T[0]-I*si*T[2]

in the expression of

exp(-I*T[0]*(omega1-2*omega2)).

However, I am only able to do so by subs command and also by exactly copying the argument in the following manner.

subs(-I*T[0]*(omega1-2*omega2) = I*omega2*T[0]-I*si*T[2], exp(-I*T[0]*(omega1-2*omega2)))

The issue is I have expressions like this all over in the main problem, and I have to copy-paste such expressions for the substitution. So I am wondering if there is a more efficient way to tackle this problem. 

Thanks in Advance,

Regards

Questions on Visualization Methods...

Asked by: jganding 135
plotting color
August 09 2023
0  0

I'm attempting to visualize temperature averages across a 2 dimentional space (e.g., a square plate) with fixed heat sources. The 3rd dimension (z axis) represents temperature.  I have created several visualizations but have questions about how these plots work.  The model is attached and the questions will make sense once you open the worksheet.

  1. Using the "colorscheme" option on a couple of matrixplots, I get the error "[Length of output exceeds limit of 1000000]" and the plot doesn't show.  However using the "display()" command on those same plots does render the plot.  Is there a way around this error (i.e., rendering the plot directly) or should I just suppress the error using a colon at the end of the plot statement and rely on display() to show the plot?
  2. I've created a heat map as one of the visualizations.  Is there a way to access the color values at each of the "cells" of the heat map? I would like to use these colors elsewhere in the model but I'm not sure if there is a way to access the color values.
  3. Using a 3D point plot as one of the visualization options, I use the colorschemes with options "xgradient", "ygradient", and "zgradient".  For some reason, "xgradient" and "ygradient" work as expected but "zgradient" looks the same as "ygradient".  How do I get the color transition to change along the z axis rather than only x and y axes?

Thank you for your help on these questions.

temperature_profile_(experimental)(v01).mw

How can I remove this error? "Error, missing opera...

Asked by: raj2018 50
July 31 2023
0  6

Hi,
Apparently I have a problem but I can't find it. Please advise what is the source of the error?
Please see the attached worksheet.
1.mw

error in Pde plot ...

Asked by: SHIVAS 35
homework pde numeric
July 29 2023
1  22
> 

restart; with(plots)
> 

``
> 

Sc := 1; sigma := 5; E := 1; delta := 1; n := .5; Pr := .71; alphac := .1; alphat := .1; Lt := .1; Br := .1; Rd := 2; deltaB := .1
``
> 

OdeSys := {(diff(Theta(xi, eta), eta, eta))/Pr+(1/2)*(1-xi)*eta*(diff(Theta(xi, eta), eta))+xi*f(xi, eta)*(diff(Theta(xi, eta), eta))-xi*(1-xi)*(diff(Theta(xi, eta), xi)), diff(h(xi, eta), eta, eta)+(1/2)*(1-xi)*eta*(diff(f(xi, eta), eta))+xi*(f(xi, eta)*(diff(h(xi, eta), eta))-(diff(f(xi, eta), eta))*h(xi, eta)-2*lambda*(diff(f(xi, eta), eta)))-xi*(1-xi)*(diff(h(xi, eta), xi)), diff(f(xi, eta), eta, eta, eta)+(1/2)*(1-xi)*eta*(diff(f(xi, eta), eta, eta))+xi*(f(xi, eta)*(diff(f(xi, eta), eta, eta))-(diff(f(xi, eta), eta))*(diff(f(xi, eta), eta))+2*lambda*h(xi, eta))-xi*(1-xi)*(diff(diff(f(xi, eta), eta), xi)), (diff(Phi(xi, eta), eta, eta))/Sc+(1/2)*(1-xi)*eta*(diff(Phi(xi, eta), eta))+xi*f(xi, eta)*(diff(Phi(xi, eta), eta))-(sigma*sigma)*xi*Phi(xi, eta)*(1+n*delta*Theta(xi, eta))*exp(-E/(1+delta*Theta(xi, eta)))-xi*(1-xi)*(diff(Phi(xi, eta), xi))}; Cond := {Phi(0, eta) = 0, Phi(xi, 0) = 1, Phi(xi, 10) = 0, Theta(0, eta) = 0, Theta(xi, 0) = 1, Theta(xi, 10) = 0, f(0, eta) = 0, f(xi, 0) = 0, h(0, eta) = 0, h(xi, 0) = 0, h(xi, 10) = 0, (D[2](f))(xi, 0) = 1, (D[2](f))(xi, 10) = 0}
> 

colour := [red, green, blue, gold]
> 

lambdaVals := [1, 1.5, 2, 3]
> 

for j to numelems(lambdaVals) do Ans[j] := pdsolve((eval([OdeSys, Cond], lambda = lambdaVals[j]))[], numeric); Ng[j] := eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j]))+Br*(xi*(eval(diff(f(xi, eta), eta), Ans[j]))-sin(xi))^2+(Br*xi*xi)*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^2-(1/3)*Br*deltaB*xi^4*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^4, lambda = lambdaVals[j]); Bj[j] := (eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j])), lambda = lambdaVals[j]))/(eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j]))+Br*(xi*(eval(diff(f(xi, eta), eta), Ans[j]))-sin(xi))^2+(Br*xi*xi)*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^2-(1/3)*Br*deltaB*xi^4*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^4, lambda = lambdaVals[j])) end do

Error, invalid input: eval received _m2939359678144, which is not valid for its 2nd argument, eqns

  
> 

 

> 

plotA := plots:-display(seq(Ans[k]:-plot(Theta(xi, eta), xi = 1, eta = 0 .. 10, color = colour[k]), k = 1 .. nops(lambdaVals)), linestyle = "solid", thickness = 2)

Error, `Ans[k]` does not evaluate to a module

  
> 

plotB := plots:-display(seq(Ans[k]:-plot(Ng[j], xi = 1, eta = 0 .. 10, color = colour[k]), k = 1 .. nops(lambdaVals)), linestyle = "solid", thickness = 2)

Error, (in pdsolve/process_depspec) specified dependent functions cannot be evaluated in terms of the PDE solution, got extra indeterminates {Ng[1]}

  
> 

plotC := plots:-display(seq(Ans[k]:-plot(Bj[j], xi = 1, eta = 0 .. 10, color = colour[k]), k = 1 .. nops(lambdaVals)), linestyle = "solid", thickness = 2 );

Error, (in pdsolve/process_depspec) specified dependent functions cannot be evaluated in terms of the PDE solution, got extra indeterminates {Bj[1]}

  
> 

``

Download error_in_plot.mw

Help me to rectify the error 

What is the mistake?

in this worksheet

linearize the complex conjugate function partial d...

Asked by: bashar27 55
linearize differential-equations conjugate
July 20 2023
0  0

restart;
alias(u = u(x, z, t), f = f(x, z, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*x);
                    /     (1/2)\           
                    \f + R     / exp(I R x)
pde1 := I*(diff(u, z))+diff(u, x, x)+diff(u, t, t)+u*abs(u)*abs(u)-(u*abs(u)*abs(u))*abs(u)*abs(u);
    / d   \              / d  / d   \\           
  I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
    \ dz  /              \ dx \ dx  //           

           / d   \                /     (1/2)\  2           
     + 2 I |--- f| R exp(I R x) - \f + R     / R  exp(I R x)
           \ dx  /                                          

       / d  / d   \\           
     + |--- |--- f|| exp(I R x)
       \ dt \ dt  //           

                                                            2
       /     (1/2)\                           2 |     (1/2)| 
     + \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

                                                            4
       /     (1/2)\                           4 |     (1/2)| 
     - \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

simplify(%);
         / d   \              / d  / d   \\           
       I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
         \ dz  /              \ dx \ dx  //           

                / d   \                 2             
          + 2 I |--- f| R exp(I R x) - R  exp(I R x) f
                \ dx  /                               

             (5/2)              / d  / d   \\           
          - R      exp(I R x) + |--- |--- f|| exp(I R x)
                                \ dt \ dt  //           

                                               2  
                                   |     (1/2)|   
          + exp(I R x - 2 Im(R x)) |f + R     |  f

                                               2       
                                   |     (1/2)|   (1/2)
          + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                               4  
                                   |     (1/2)|   
          - exp(I R x - 4 Im(R x)) |f + R     |  f

                                               4       
                                   |     (1/2)|   (1/2)
          - exp(I R x - 4 Im(R x)) |f + R     |  R     
collect(%, exp(I*R*x));
  /  (5/2)       / d   \      2       / d   \   / d  / d   \\
  |-R      + 2 I |--- f| R - R  f + I |--- f| + |--- |--- f||
  \              \ dx  /              \ dz  /   \ dx \ dx  //

       / d  / d   \\\           
     + |--- |--- f||| exp(I R x)
       \ dt \ dt  ///           

                                          2  
                              |     (1/2)|   
     + exp(I R x - 2 Im(R x)) |f + R     |  f

                                          2       
                              |     (1/2)|   (1/2)
     + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                          4  
                              |     (1/2)|   
     - exp(I R x - 4 Im(R x)) |f + R     |  f

                                          4       
                              |     (1/2)|   (1/2)
     - exp(I R x - 4 Im(R x)) |f + R     |  R     
 

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