I have two equations developed in different ways and I want to compare them.
The first is a development done using maple, while the second is an algebraic analysis.

I need to find out if both are identical and, therefore, if the subtraction would be equal to zero.

How should I proceed?

I had thought about simplifying the first and comparing it with the second; is that a good approach?

Download TESTE_MAPLE.mw

my question is a little bit long but is not complicated, i want find thus  unkown but  realy i am don't know how apply on it by maple, i have two best paper which explain very well i just want to find thus dimensional Lie algebra which is be invariant or not satisfy condition or not which i have to used or which i have not to use it also the importan part how find them in paper 1 first , for equation fisher 
How find eq(29) which is i think is two -dimensional Lie algebra of equation, also the best part is reduction which by apply this we can change PDE to ode but i don't know how apply eq(31) or even find it yet  is related to eq(27-28)  and by replacing equation eq(34) we can get our ode i am just loking for the ode, for the eq(76) and eq(85) have same procedures,  i will mention the paper link too 

Lie.mw

paper-1

paper-2

Hi,

I am trying to reproduce a polar curve, as shown in the attached picture.
I have tested several polar expressions and different plotting options in Maple, but I can’t manage to obtain an exact match, 

If you have any ideas about a possible polar equation, a combination of functions, or plotting parameters (sampling, domain, polarplot options, etc.), I would be very grateful.

Thanks in advance for your help!

Q_Polar.mw

I am trying to calculate the stability of my solution using this integral test:

U = 1/2 * ∫ u(x,t)^2 dx

Then I want to compute the derivative with respect to epsilon and check if the result is greater than zero or less than zero.

I tried to do it in Maple but it is not working correctly.

Also, I want to substitute random numbers for the parameters to test stability. I prefer to use simple integer values like 1, 2, 3, etc., not decimal numbers. When I try random values, sometimes the result does not evaluate or gives complicated output.

S-test.mw

In the attached file, I want to calculate the integral Q1. Numerically, this is easy to do in Maple. For theoretical reasons, the exact result pi/e is known. However, a contradiction arises between command lines (4) and (5). Command (6) is also unsuccessful, as its exact result is unknown. What am I doing wrong?

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is been a while i work on it but i can't figure out where is problem and even my solution is so far from it when numerically i tested , i got same outcome as the paper did maybe is  long but it is same and maybe have some typical different but they are same , the problem in here is that which when i substitue is not my answer i don't know where is my mistake ?

pde-te.mw

f18.mw

f19.mw

The plot in the attached file only works if the complete function expression is entered. If only the function name is entered, no plot appears. What am I doing wrong?test.mw

Download test.mw

Hi,

I’m trying to transpose an existing animation that connects the unit circle to the graphs of cos⁡(θ)\ and sin⁡(θ)\ into a complex-numbers visualization, so that students can clearly see the link between

z=eiθ=cos⁡θ+isin⁡θ,arg⁡(z)=θ,∣z∣=1

and the corresponding real/imaginary components.

Goal: a dynamic view where a point z(θ) moves on the unit circle in the complex plane while (simultaneously)

• the projections show ℜ(z)=cos⁡θ\  and ℑ(z)=sin⁡θ,

•  the graphs of cos⁡θ and sin⁡θ are traced against θ\,

• and/or the angle θ\ and argument are displayed in a clean, didactic way.

To better illustrate my objective, here is the link to the target animation I would like to transpose: 

Illustration

Thank you in advance for your insights and feedback.

Animation_Question.mw

Hello everyone
Dear experienced and expert friends
As a beginner, I would like to ask if any of my friends can guide me.
The following commands are related to Mathematica:

plots = Table[n = sValues[[i]];
   ParametricPlot[{1 - 2/n - 1.5/n^2 + (1.33 - 2/n) \[Gamma] - 
      0.0740741 (15 + 4*n) \[Gamma]^2, 
     12/n^2 + (16 \[Gamma])/n + (80 \[Gamma]^2)/9}, {\[Gamma], 0, 
     0.06}, PlotStyle -> colors[[i]], 
    PlotRange -> {{-10, 10}, {-10, 10}}], {i, Length[sValues]}];

Show[plots, Frame -> True, FrameLabel -> {"\!\(\*
StyleBox[SubscriptBox[\"n\", \"s\"],\nFontSize->16,\n\
FontColor->GrayLevel[0]]\)", "\!\(\*
StyleBox[\"r\",\nFontSize->16,\nFontColor->GrayLevel[0]]\)"}, 
 GridLinesStyle -> Black, PlotRange -> {{0.94, 1}, {0, 0.06}}, 
 PlotLegends -> 
  Placed[LineLegend[sValues, LegendLabel -> "s,w"], {0.5, 0.5}], 
 ImageSize -> 400]

I want to rewrite this process in Maple for my own functions.
I would be grateful if it is possible or if these commands are rewritten in a complete and executable form in Maple for me so that I can understand the working pattern. Or at least an equivalent command that can do this in Maple is introduced
Thank you all

Hi,
I’m taking the liberty of getting back to you once again regarding the animation of a procedure (here, for fractals). I’m able to use the Explore command correctly, but I’m having difficulty with animate.
Thank you very much for your help — it is truly invaluable.

Q_Fractales.mw

Hi,
I’d appreciate your insights on how to animate this sequence (family) of functions in order to obtain a rendering like the one shown below.

Any suggestions or best practices would be very welcome. Thank you!

AnimQ.mw

What does Error, (in dsolve/numeric/bvp) bad index into Matrix mean?
Also, I'm trying to run it, it is slow, any suggestions?

restart;
with(Student[VectorCalculus]);
with(DynamicSystems);
with(DEtools);
with(PDEtools, ReducedForm, declare, diff_table, dsubs);
NULL;
 #Digits:= trunc(evalhf(Digits)); #generally a very efficient setting

# Here we solve a 1D problem in 3 regions. In each region, we have concentration and potential (c,phi) distributions,
# We first solve the unperturbed steady-state problem and then the linearized perturbation problem (which rely on the steady state).
# Each region is defined in x = 0..1, and the regions are connected by interface conditions that 
# connect (c1(1),phi1(1)) to (c2(0),phi2(0)) and (c2(1),phi2(1)) to (c3(0),phi3(0))

Q:=10;   omega:=100;     J0:= 0.01;   # parameters
                            Q := 10

                          omega := 100

                           J0 := 0.01

# The unperturbed steady-state

c1:=1-J0/2*x: 
c3:=1-J0/2*(x-1):  
c12:= eval(c1,x=1); 
c32 := eval(c3,x=0); 
S1:=sqrt(Q^2+4*c12^2): 
S3:=sqrt(Q^2+4*c32^2):  
c21:=eval((S1-Q)/2); 
c23:=eval((S3-Q)/2);  
I0:=fsolve(Q*i0/2/J0*ln((J0*S1-Q*i0)/(J0*S3-Q*i0))=(J0-S1+S3)/2,i0);  
V:=(I0/J0+1)*ln(c32/c12)+ln((c21+Q)/(c23+Q))+(J0+2*c23-2*c21)/Q; # the potential drop across the system 
c2:=solve(y-c21+Q*I0/2/J0*ln((Q*I0-Q*J0-2*J0*y)/(Q*I0-Q*J0-2*J0*c21))=-J0/2*x,y):  
phi1:=I0/J0*ln(c1)+V: 
phi3:=I0/J0*ln(c3): 
dphi1:=diff(phi1,x); 
dphi3:=diff(phi3,x); 
phi21:=I0/J0*ln(c12)+V-0.5*ln((c21+Q)/c21); 
phi2:=(2*c21-2*c2+Q*phi21-J0*x)/Q: 
dphi2:=diff(phi2,x); 
dphi12 := eval(dphi1, x=1); 
dphi21 := eval(dphi2, x=0); 
dphi23 := eval(dphi2, x=1); 
dphi32 := eval(dphi3, x=0); 
INT1 := int(1/(2*c1), x = 0 .. 1); 
INT2 := int(1/(2*c2 + Q), x = 0 .. 1); 
INT3 := int(1/(2*c3), x = 0 .. 1); 
INT := INT1 + INT2 + INT3;
                      c12 := 0.9950000000

                       c32 := 1.005000000

                      c21 := 0.09804129000

                      c23 := 0.1000024500

                      I0 := 0.01419804328

                       V := 0.02539628566

                              0.007099021640   
                dphi1 := - --------------------
                           1 - 0.005000000000 x

                              0.007099021640        
           dphi3 := - ------------------------------
                      1.005000000 - 0.005000000000 x

                     phi21 := -2.299074561

dphi2 := (0.001000000000 LambertW(-0.2818670588 exp(-0.2818670588

   - 0.0007043224058 x)))/(1

   + LambertW(-0.2818670588 exp(-0.2818670588 - 0.0007043224058 x)

  )) - 0.001000000000

                   dphi12 := -0.007134695118

                   dphi21 := -0.001392499832

                   dphi23 := -0.001391964358

                   dphi32 := -0.007063703124

                      INT1 := 0.5012541824

                     INT2 := 0.09805801917

                      INT3 := 0.4987541511

                       INT := 1.098066353

sys1 := {
-omega*C11(x)+diff(diff(C12(x), x), x)=0,
omega*C12(x)+diff(diff(C11(x), x), x) = 0,
-omega*C21(x)+diff(diff(C22(x), x)+(c2*sigma2-C22(x)*dphi2*Q)/(2*c2+Q), x) =0,
 omega*C22(x)+diff(diff(C21(x), x)+(c2*sigma1-C21(x)*dphi2*Q)/(2*c2+Q), x) = 0,
-omega*C31(x)+diff(diff(C32(x), x), x)=0,
omega*C32(x)+diff(diff(C31(x), x), x) = 0
}:

sys2 := {
diff(FA1(x), x) = C11(x)*dphi1/c1,
diff(FA2(x), x) = C21(x)*dphi2/(c2+Q/2),
diff(FA3(x), x) = C31(x)*dphi3/c3,
diff(FB1(x), x) = C12(x)*dphi1/c1,
diff(FB2(x), x) = C22(x)*dphi2/(c2+Q/2),
diff(FB3(x), x) = C32(x)*dphi3/c3
}: 

Bc := {
C11(0) = 0, C12(0) = 0,  C31(1) = 0, C32(1) = 0,
FA1(0) = 0, FB1(0) = 0,  FA3(1) = 0, FB3(1) = 0, 

2*C11(1)/c12 = C21(0)/(c21+Q)+C21(0)/c21, 
2*C12(1)/c12 = C22(0)/(c21+Q)+C22(0)/c21,
C21(1)/(c23+Q)+C21(1)/c23 = 2*C31(0)/c32,
C22(1)/(c23+Q)+C22(1)/c23 = 2*C32(0)/c32,

D(C11)(1)+dphi12*C11(1)-sigma1/2-c12*D(FA1)(1) = D(C21)(0)+dphi21*C21(0)-(c21+Q)*sigma1/(2*c21+Q)-(c21+Q)*D(FA2)(0),
D(C12)(1)+dphi12*C12(1)-sigma2/2-c12*D(FB1)(1) = D(C22)(0)+dphi21*C22(0)-(c21+Q)*sigma2/(2*c21+Q)-(c21+Q)*D(FB2)(0),
D(C11)(1)-dphi12*C11(1)+sigma1/2+c12*D(FA1)(1) = D(C21)(0)-dphi21*C21(0)+c21*sigma1/(2*c21+Q)+c21*D(FA2)(0),
D(C12)(1)-dphi12*C12(1)+sigma2/2+c12*D(FB1)(1) = D(C22)(0)-dphi21*C22(0)+c21*sigma2/(2*c21+Q)+c21*D(FB2)(0),

D(C31)(0)+dphi32*C31(0)-sigma1/2-c32*D(FA3)(0) = D(C21)(1)+dphi23*C21(1)-(c23+Q)*sigma1/(2*c23+Q)-(c23+Q)*D(FA2)(1),
D(C32)(0)+dphi32*C32(0)-sigma2/2-c32*D(FB3)(0) = D(C22)(1)+dphi23*C22(1)-(c23+Q)*sigma2/(2*c23+Q)-(c23+Q)*D(FB2)(1),
D(C31)(0)-dphi32*C31(0)+sigma1/2+c32*D(FA3)(0) = D(C21)(1)-dphi23*C21(1)+c23*sigma1/(2*c23+Q)+c23*D(FA2)(1),
D(C32)(0)-dphi32*C32(0)+sigma2/2+c32*D(FB3)(0) = D(C22)(1)-dphi23*C22(1)+c23*sigma2/(2*c23+Q)+c23*D(FB2)(1)
}:
 
 

all_sys := sys1 union sys2 union Bc:
sol1 := dsolve(all_sys, initmesh = 100, maxmesh = 15000, numeric, method = bvp[midrich], output = listprocedure):
#(all_sys, numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) bad index into Matrix

I'm looking for the general solution to the attached differential equation. Maple doesn't provide it. What am I doing wrong?

Download testdgl5.mw

this transforamtion including two function which i try to do, but my result is so different and even is not near i did like the author mention but i don't know how reach that outcome, the importan part is the equation 2.7

s1.mw

in here i want to apply this method for finding my parameter but is a special kind of substituion and i don't know how hundle this kind  and find the parameters i did some part but i didn't reach the target 

f-p-second.mw