Before at most a year i asked about this applying long wave limit which is coming from some kind of series which i am not sure to how get this result from the series but i provide just the two function of series for appyting the long wave limit and then we can generalized to N value of them, i asked to Ai too he give me a good explanation and somehow he did programing but  i am not cool with programing of Ai,  i  am looking for result eq14 and eq 20 , i have a series for eq(12) N=2 and for other N too but by applying long wave limit it is become to eq(14) and then F[4] becone to eq(20) i want that result by don't have any idea how reach it  

Long-wave-limit-testing.mw

Ai-result.mw

update F4

In the attached file "test," a system of ordinary differential equations is solved. I was able to create the (r, phi) plot. But how are the (t, r(t)) and (t, phi(t)) plots executed with the calculation results?
What does "range" mean in the (r, phi) plot command? Is there a more precise numerical method than the Runge-Kutta method used in "test" (perhaps a finer t-division of the axis?)?

Download test.mw

Maple documents appear to be an excellent way of documenting problems and procedures, and notetaking in general, but I have always found them laborious and frequently encountered problems with formatting. One may as well use Tex. This is the reason that I was struck by the ability of the GenerateDocument() procedure in the NaturalLanguage package to create Maple documents.

Is there any practical way to use NaturalLanguage for notetaking and documentation of procedures. By this I mean, the ability to input math and or explanatory text and request(direct) the AI to produce a maple document.

dear sir here i am giving python code exicuting 3d plots but i cant plot animations like

restart;
Nc := .3; M := 1.5; QG := 1.5; Thetaa := .2; n1 := 1; n2 := 0; lambda1 := .1; lambda2 := .1; lambda3 := .1;

p := 2; a := .5; alpha1 := (1/2)*Pi;

p1 := 0.1e-1; p2 := 0.1e-1;
rf := 997.1; kf := .613; cpf := 4179; betaf := 21*10^(-5);

betas1 := .85*10^(-5); rs1 := 3970; ks1 := 40; cps1 := 765;
betas2 := 1.67*10^(-5); rs2 := 8933; ks2 := 401; cps2 := 385;

z1 := 1/((1-p1)^2.5*(1-p2)^2.5);
knf := kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1)); khnf := knf*(ks2+2*knf-2*p2*(knf-ks2))/(ks2+2*knf+p2*(knf-ks2));
z2 := 1-p1-p2+p1*rs1/rf+p2*rs2/rf;
z3 := 1-p1-p2+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf);
z4 := khnf/kf;
z5 := 1-p1-p2+p1*rs1*betas1/(rf*betaf)+p2*rs2*betas2/(rf*betaf);
OdeSys := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond := {Theta(0, tau) = 1+a*sin(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
OdeSys1 := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond1 := {Theta(0, tau) = 1+a*sin(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
OdeSysa := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Conda := {Theta(0, tau) = 1+a*cos(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
OdeSysa1 := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Conda1 := {Theta(0, tau) = 1+a*cos(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};

colour := [cyan, black];
colour1 := [red, blue];
NrVals := [2.5, 3.5];
for j to numelems(NrVals) do Ans := pdsolve((eval([OdeSys, Cond], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plots[j] := Ans:-plot(Theta(X, tau), tau = .8, linestyle = "solid", labels = ["Y", Theta(Y, tau)], color = colour[j], 'axes' = 'boxed'); eta[j] := Ans:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n1*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "solid", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour[j]); Ans1 := pdsolve((eval([OdeSys1, Cond1], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plots1[j] := Ans1:-plot(Theta(X, tau), tau = .8, linestyle = "dash", labels = ["Y", Theta(Y, tau)], color = colour[j], 'axes' = 'boxed'); eta1[j] := Ans1:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n2*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "dash", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour[j]); Ansa := pdsolve((eval([OdeSysa, Conda], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plotsa[j] := Ansa:-plot(Theta(X, tau), tau = .8, linestyle = "solid", labels = ["Y", Theta(Y, tau)], color = colour1[j], 'axes' = 'boxed'); etaa[j] := Ansa:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n1*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "solid", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour1[j]); Ansa1 := pdsolve((eval([OdeSysa1, Conda1], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plotsa1[j] := Ansa1:-plot(Theta(X, tau), tau = .8, linestyle = "dash", labels = ["Y", Theta(Y, tau)], color = colour1[j], 'axes' = 'boxed'); etaa1[j] := Ansa1:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n2*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "dash", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour1[j]) end do;
plotA := plots:-display([seq(Plots[j], j = 1 .. 2)]);
plotB := plots:-display([seq(Plots1[j], j = 1 .. 2)]);
plotAA := plots:-display([seq(Plotsa[j], j = 1 .. 2)]);
plotBB := plots:-display([seq(Plotsa1[j], j = 1 .. 2)]);
plotC := plots:-display([seq(eta[j], j = 1 .. 2)]);
plotD := plots:-display([seq(eta1[j], j = 1 .. 2)]);
plotCC := plots:-display([seq(etaa[j], j = 1 .. 2)]);

plotDD := plots:-display([seq(etaa1[j], j = 1 .. 2)]);
plots:-display([plotA, plotB, plotAA, plotBB], size = [700, 700]);

plots:-display([plotC, plotD, plotCC, plotDD], size = [700, 700]);

how to take animation of the plots

i have seen some plots in maple also for that reason i have posted this question here

paper2_new_efficiency_plots_2025.mw

Hi,
I want to solve equations (1) and (2) to obtain the values of certain quantities, for example x and f. In fact, both equations must be satisfied simultaneously for \tau and f. Since there are other parameters in these equations (for example \tau, M, etc.), and I do not know the optimal values of these parameters, I would like to solve equations (1) and (2) over given ranges for tau, M, and so on. I know that I should use loop commands, but I keep encountering errors. Please guide me.
fsolve.mw

In this kind of contour plot i have two line but when i change time variable t just contour of one line wil move the other is not do any movement and is stop how i can  make the second plot one second line move too? also there is any way for ploting this kind any other option?

line-2-done.mw

Hello everyone

I have the following probability distribution, where x ranges from zero to infinity:

with(Statistics):

X := RandomVariable(Distribution(PDF = unapply(piecewise(And(0 < x, x < infinity), exp(-6)*6^x/x!), x)))

How do I tell Maple that this distribution is discrete?

Regards,

Oliveira

I have a function that calculates a volume in mm^3, but for the purposes of plotting, I would like to plot the values as m^3.

How do I specify that the units to be plotted are m^3, have Flow convert the values to m^3, from mm^3 and show that the units for the axis are m^3?

I have tried using the useunits[m,m^3] function, but the graph does not change the value of the units, and it does not display the units of the result on the graph axis.

Also, is there a good quick reference for all of the options available for the plot command?  The user manual has very little, and the tutorial file only gives limited examples also.

I am trying to integrate a function in Maple Flow, that uses units.

When I use units of metres, the integration works.  If I mix the units, or I use millimetres throughout the equation, it does not work.

I have attached the sample worksheet, which shows the problem.

CrossSectionalDeepDive.flow.zip

The following problem is old and quite challenging. I found it in a publication from 1959. I have the source and my own solution. I was able to solve it quite laboriously a few years ago using MC14 – but not recently with Maple. Therefore, I'm interested in instructive Maple solutions, just as previous puzzle solutions here have helped me further in using this software. I thank you for that.

A wolf observes a goat. It is grazing in a meadow, tied to a rope. Naturally, he wants to catch the goat and considers whether his starting position is favorable. He estimates that he and the goat will be moving at the same speed at the beginning of the hunt and throughout the pursuit, and that the goat will constantly hold the rope taut to maintain its distance for escape reasons. Now, as he approaches the goat at a constant top speed, the same speed as the goat is fleeing in a circular arc, he asks himself: Where do I need to start from to guarantee success? Are there starting positions that rule out a successful hunt? What happens if I manage to sneak into the grazed area first?

i did for two of them base on the information but one of them is not make my odetest to be zero? where is problem

test.mw

I have already plotted the Nusselt number as a line graph. Now, I would like to plot it as a bar graph instead of line graphs. Specifically, I want to create grouped bar charts that combine several parameters (such as Gr, Rb, N[t], N[r], M, Sc) in a single figure. Each group should correspond to one parameter, with bars representing distinct values (e.g., 0.1, 0.4, 0.6, 0.8). For reference, I have attached a sample figure from another work. Could anyone please help in this regard?

Group_bar_graphs_help.mw

How do I enter a number as an actual percentage?  I know that I can enter a number as a fraction, and then redisplay the number formatted as a percentage, but I would like to be able to type in that a variable is 10%, not have to type in that it is 0.1, then convert it to percent.  I would like Maple Flow to figure out what it is, because I typed in, in effect, it's units.

In the plane, the concentric circles k1 and k2 are given with center M. Circle k1 is the unit circle (radius = 1), and k2 has twice the area of ​​k1. From the outside, five congruent circles k3 are placed tangent to k1, each with a radius r yet to be calculated. Prove that the circles k3 can be arranged such that any two adjacent circles k3 and k2 can have a common intersection point, and these intersection points form the vertices of a regular pentagon. The radius r is to be calculated exactly (no approximation) as a term.

Suppose I have a metric g, and I want to perform a conformal transformation g = exp(2Phi(X))*g, is there a straightforward way to do this for curvature quantitieies (Christoffel, Ricci Scalar etc)? I was able to do it rather easily for the Christoffel symbols, as seen below, but it required me making a substitution for each index pair. While this isn't horrible, it would be nice if there was a way to do it without this procedure.

** Edited to make it Phi(X) 

Any thoughts appreciated, thank you!

MyConformal.mw