## a problem with a BVP problem...

Hi dear maple users
I have a BVP problem, how can get this problem solved?

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## How do I solve a Elzaki transform partial differen...

```ElzakiTransform := proc(f, t) int(f*exp(-t/v)*v, t = 0 .. infinity); end proc; f := e^(n*t); result := ElzakiTransform(f, t); result;```

Is this true?

## How do you change the font size of labels on axe...

For_MaplePrimes_question.mw

In the above Maple document, I present a puzzling problem:  When I use plot3d, the options

font = [Times, bold, 16], labels = ['u', 'v', 'z'], labelfont = [Times, bold, 40] in the command

with(plots);
plot3d([u*sin(2*v), u^2, u*cos(2*v)], transparency = 0.60, shading = none, font = [Times, bold, 16], labels = ['u', 'v', 'z'], labelfont = [Times, bold, 40], grid = [60, 60]);

produces nice big labels on the axes, which are visible as opposed to the almost invisible default size, especially on printouts but when I use these options as in below command:

fieldplot3d([0, 0, -y], x = -2 .. 2, y = -2 .. 2, z = -2 .. 2, arrows = `3-D`, fieldstrength = maximal(0.5), font = [Times, bold, 16], labels = ['x', 'y', 'z'], labelfont = [Times, bold, 40], grid = [4, 4, 4])

the lables x, y and z on the fieldplot are small, the default.  I used the same option and get different results.

I have been researching this for almost 2 hours and I can't find a way to increase the font size in the fieldplot command.

Is this a bug or does the fieldplot command not use these options the way it is used in the plot3d command?

Thank You for reading my question. (I am relatively inexperienced with Maple.)

Tom K.

## How to enable backups in Maple?...

I somehow managed to turn off autosave some time ago. Now I have reenabled it, but Maple still doesn't create any backups. Am I missing something?

Any help is appriciated.

## How can we convert between mtx-format and graph-fo...

There are various variants of graph coloring, such as when I want to compute the star chromatic number of a graph, Maple (or Mathematica) seems not to provide relevant functions.

Fortunately, the software ColPack   offers this functionality （Note: I just noticed that this software also uses greedy coloring instead of accuracy）. However, it supports the MTX format. So, the question is:

•  How can I write a graph in MTX format?

And

•  how can the MTX format be converted into a graph format?

Of course, I would like to perform these operations in Maple.  (SageMath may have something)

The following is an example (bcsstk01.mtx） in the directory `ColPack-master/Graphs directory` of the source code of ColPack.

bcsstk01.mtx.txt

```./ColPack -f ../../Graphs/bcsstk01.mtx -m STAR
Out: 11```

But I do not know what the graph in the example is. On the contrary, I would like to compute the star chromatic number of the Petersen graph, and I also don't know how to convert it into the MTX format like the above.

```with(GraphTheory):
with(SpecialGraphs):
P:=PetersenGraph()```

I don't understand what the very long decimal numbers (like `2.8322685185200e+06`) in the third column in the MTX-file. Will it affect the  imformation of the entire graph?

For MTX format, see https://math.nist.gov/MatrixMarket/formats.html.  For graphs, the numbers in the third column can all be considered as 1 (with the first two columns representing vertices, and their adjacency). Of course, this is my interpretation and may not necessarily be correct.

## How to Convert PDE to ODE?...

How to conver a patial differetial equation to ordinary differential equation with or without dchange?

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## Questions on applying identities from the Function...

I make more and more use of the FunctionAdvisor. I have started to apply rules from the advisor to expressions. Here are two examples with questions:

Expression to apply an identiy to

 (1)

 (2)

 (3)

Using the following identity from Maples FunctionAdvisor and the correspondence in (3)

 (4)

 (5)

That worked. Q1: But is it a good way to do so?

Now  a new example: Converting InverseJacobinAM to InverseJacobiSN

 (6)

 (7)

 (8)

 (9)

This is of course wrong since comparing the InverseJacobiAM expression in (6) and (7)  should be

 (10)

 (11)

Q2: How to avoid simplification of to

## Numerical solution of systeem of PDEs with Robin-t...

Dear Users!

I hope everyone is fine here. I want to solve the following system of PDEs associated with Robin-type boundary conditions. But got the error. Kindly help me to fix this issue. Thanks

restart; TT := 0.1e-2; l := 1/5; b[1] := .18; b[2] := 2*10^(-9); k[1] := 1.3*10^(-7); k[-1] := 24; k[2] := 7.2; p := .9997; d[1] := 0.412e-1; f := .2988*10^8; g := 2.02*10^7; s := 1.36*10^4; E[0] := 3.3*10^5; T1[0] := .5*10^9; C1[0] := 3.3*10^5; alpha[0] := 10^(-10); D1 := 10^(-6); D2 := 10^(-2); D3 := 10^(-6); d[4] := 1.155*10^(-2); t[0] := 1/D1; kappa := 10^4; k[3] := 300*(24*60); chi := 0; sigma := d[1]*t[0]; rho := f*t[0]*C1[0]/(E[0]*T1[0]); mu := k[1]*t[0]*T1[0]; eta := g/T1[0]; epsilon := t[0]*C1[0]*(p*k[2]+k[-1])/E[0]; omega := D3/D1; beta1 := b[1]*t[0]; beta2 := b[2]*T1[0]; phi := k[1]*t[0]*E[0]; lambda := t[0]*C1[0]*(k[-1]+k[2]*(1-p))/T1[0]; psi := t[0]*(k[-1]+k[2]); gamma1 := chi*alpha[0]/D1; delta := D2/D1; kappa := k[3]*t[0]*C1[0]/alpha[0]; xi := d[4]*t[0]; PDE1 := diff(u(y, t), t) = diff(u(y, t), y, y)-gamma1*(u(y, t)*(diff(theta(y, t), y, y))+(diff(u(y, t), y))*(diff(theta(y, t), y)))+sigma*piecewise(y <= l, 0, 1)+rho*C(y, t)/(eta+T(y, t))-sigma*u(y, t)-mu*u(y, t)*T(y, t)+epsilon*C(y, t); PDE2 := diff(theta(y, t), t) = delta*(diff(theta(y, t), y, y))+kappa*C(y, t)-xi*theta(y, t); PDE3 := diff(T(y, t), t) = omega*(diff(T(y, t), y, y))+beta1*(1-beta2*T(y, t))*T(y, t)-phi*u(y, t)*T(y, t)+lambda*C(y, t); PDE4 := diff(C(y, t), t) = mu*u(y, t)*T(y, t)-psi*C(y, t); ICs := u(y, 0) = piecewise(0 <= y and y <= l, 0, 1-exp(-1000*(x-l)^2)), T(y, 0) = piecewise(0 <= y and y <= l, 1-exp(-1000*(x-l)^2), 0), C(y, 0) = piecewise(l-epsilon <= y and y <= l+epsilon, exp(-1000*(x-l)^2), 1-exp(-1000*(x-l)^2)), theta(y, 0) = 0; BCs := {(D[1](C))(0, t) = 0, (D[1](C))(1, t) = 0, (D[1](T))(0, t) = 0, (D[1](T))(1, t) = 0, (D[1](theta))(0, t) = 0, (D[1](theta))(1, t) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = 0};

PDE:= {PDE1, PDE2, PDE3, PDE4}; pds := pdsolve(PDE, {ICs}, BCs, numeric, spacestep = 1/100, timestep = 1/100);

Error, (in pdsolve/numeric/process_PDEs) specified dependent variable(s) {(D[1](C))(0, t) = 0, (D[1](C))(1, t) = 0, (D[1](T))(0, t) = 0, (D[1](T))(1, t) = 0, (D[1](theta))(0, t) = 0, (D[1](theta))(1, t) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = 0} not present in input PDE

## Simplify or factor of (3a - 3)...

Good afternoon, I'm trying to simplify or that Maple gives me the factor of (3a - 3) and it doesn't. The result that should be thrown is 3(a-1).

Hi.

When trying to open my document it says:

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

## Long waiting time of plotting the chen–gackstatter...

Hello do u know how to make this code more optimal? this is very long time to plot.

g := evalf((Beta(1/4, 1/4)/2)^4);

A := Pi*r*cos(theta) - Re(WeierstrassZeta(r*exp(theta*I), g, 0) + Pi*WeierstrassPPrime(r*exp(theta*I), g, 0)/g);
B := Pi*r*sin(theta) + Im(WeierstrassZeta(r*exp(theta*I), g, 0) - Pi*WeierstrassPPrime(r*exp(theta*I), g, 0)/g);
C := sqrt(6*Pi/g)*Re(WeierstrassP(r*exp(theta*I), g, 0));

plot3d([A, B, C], r = 1/5 .. 4/5, theta = -Pi .. Pi, view = [-8 .. 8, -8 .. 8, -8 .. 8], shading = zhue, grid = [200, 200]);

## How do I test against the specified tolerance?...

Good day everyone.

I am trying to write a code with variable stepsize involving tolerance. two vectors are declare for the errors. However, I don't know how to declare the two errors in comparison with the tolerance. Please kindly help. Also, any other modification to the entire code is also welcomed. Thank you all and best regards.

The code is as attached.

Variable_step_size_Falkner.mw

## Plot line symbols disappear in legend ...

Dear Maple experts,

I am running a Maple code with several lines/ curves in a plot.

For two of the curves, I use style=pointline. But in the legend the symbols on the lines are not shown. Can you advise how we can make them appear?

I have attached the file. Thank you so much!

## how to plot these equations ...

i want to plot this equations for P and t for  t= 0 t0 600 seconds..can u provide me how?

time-dependent_aerodynamic_pressure.mw

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## How to split a square Matrix...

Hi!

I hope everyone is fine. I have a square matrix like the following form
A := Matrix([[10, -1, 2, 0], [-1, 11, -1, 3], [2, -1, 10, -1], [0, 3, -1, 8]]);
How to split A into three matrices D, L and U as:

D:= Matrix([[10, 0, 0, 0], [0, 11, 0, 0], [0, 0, 10, 0], [0, 0, 0, 8]]);
L := Matrix([[0, 0, 0, 0], [-1, 0, 0, 0], [2, -1, 0, 0], [0, 3, -1, 0]]);
U := Matrix([[0, -1, 2, 0], [0, 0, -1, 3], [0, 0, 0, -1], [0, 0, 0, 0]]);