Maple Questions and Posts

How find true parameter which satisfy pde?...

Asked by: salim-barzani 950

January 28 2025

0 2

>

(1)

>

(2)

>

(3)

>

(4)

>

(5)

>

LL := diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x)-(diff(diff(diff(f(x, y, z, t), x), x), x))-(diff(diff(diff(f(x, y, z, t), t), t), x))-(diff(diff(diff(f(x, y, z, t), t), x), x))-2*(diff(diff(diff(f(x, y, z, t), t), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), z))-(diff(diff(diff(f(x, y, z, t), x), y), y)) = 0

(6)

>

S22 := f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)

f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)

(7)

>

(8)

>

(9)

>

${t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2), (4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2), exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)}$

(10)

>

eq2 := algsubs(exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z) = X, L4)

(11)

>

-(1/2)*(k[1]+k[2])*B[1]*((k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-8*k[1]*k[2]^3-12*k[2]^2*k[1]^2+(-8*k[1]^3+3*k[1]+2*s[1])*k[2]+2*s[2]*k[1])*exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = 0

(12)

>

${t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2), exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2]))}$

(13)

>

eq4 := algsubs(exp((1/2)*t*sqrt(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))+(1/2)*t*sqrt(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = V, eq3)

-(1/2)*(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])*V = 0

(14)

>

${V, B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(15)

>

eqs := {coeffs(collect(numer(normal(lhs(eq4))), {V}, 'distributed'), {V})}; nops(%); indets(eqs)

${-(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])}$

${B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(16)

>

${B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

Warning, solving for expressions other than names or functions is not recommended.

${B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = 0, k[1] = k[1], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = B[1], k[1] = k[1], k[2] = k[2], s[1] = (1/2)*(8*k[2]*k[1]^3+12*k[2]^2*k[1]^2+8*k[1]*k[2]^3-3*k[1]*k[2]-2*s[2]*k[1]-(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))/k[2], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(17)

>

${B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(18)

>

(19)

Download hard_parameters.mw

It's just a cube!...

Asked by: Alfred_F 280

January 28 2025

1 4

Inspired by the task "With two cuts into 4 equal areas" I remember the following old task:

How can you divide a cube into 6 pyramids so that their volumes are 1 : 2 : 3 : 4 : 5 : 6?

Grid with numnodes option does not create files...

Asked by: nm 11023

January 28 2025

1 5

I've been evaluating Grid but I found some problems with SQLite DB when not using numnodes.

So I am now using numnodes option to setup explicitly number of nodes to use with Grid.

But the problem is now print() do not show on the screen from node code. So hard to debug. So I changed code to send debug messages to print files.

But now I find that the files do even get created when using numnodes.

When removing numnodes option, the text file gets created.

I am using FileTools:-Text:-WriteString() and FileTools:-Text:-Close() in the node code.
I also tried using fopen(). Both do not work.

Same code works OK if I do not use numnodes.

Any idea why the file do not get created when using numnodes? Worksheet to produce this is below.

I use C:\\tmp folder for testing. Feel free to change this. When I run the code and look in the folder, I do not see the text file there when using numnodes.

It is possible the file is created but saved somewhere else on the system even though the full file name is given?

It seems to me now that when using numnodes option, there are some things that work and some things that do not work. I do not know if this is by design or a bug. Any one knows?

>

restart;

>	interface(version);

>	Physics:-Version();

Why task running on node do not create text file?

>

restart;

>	currentdir("C:\\TMP"): #change as needed

>	foo:=proc(n::integer) local file_name::string; currentdir("C:\\TMP"): #change as needed file_name:=cat(currentdir(),"\\",n,"_file.txt"); FileTools:-Text:-WriteString(file_name,cat("processing at node =",n)); FileTools:-Text:-Close(file_name); end proc:

>	Grid:-Set(foo): Grid:-Setup("local",numnodes=1); Grid:-Run(0,foo,[0]): Grid:-Wait();

>	#No file "0_file.txt" is created in my C:\\TMP\ folder

>

Another version using fopen instead of FileTools. This also do not work

>

restart;

>	currentdir("C:\\TMP"): #change as needed

>

foo:=proc(n::integer)
   local file_name::string, fileID;
   currentdir("C:\\TMP"): #change as needed
   file_name:=cat(currentdir(),"\\",n,"_file.txt");
   try
        fileID := fopen(file_name,WRITE);
    catch:
        error StringTools:-FormatMessage(lastexception[2..-1]);
    end try;

   fprintf(fileID,"%s",cat("processing at node =",n));
   fclose(fileID);
end proc:

>	Grid:-Set(foo): Grid:-Setup("local",numnodes=1); Grid:-Run(0,foo,[0]): Grid:-Wait();

Download grid_question_jan_29_2025.mw

To see the file 0_file.txt get created in the folder, simply remove the numnodes option.

News from Tangens...

Asked by: Alfred_F 280

January 27 2025

2 3

We are looking for all triangles (with the exception of similarity) in which the tangent values of the interior angles are all integers.

Area Intersection Point with vector ...

Asked by: romanrieme 50

January 27 2025

0 4

Hello
I am a bit further with my initial vector question. I managed to decompose the vectors and set them as equations for each dimension (x, y, z) and solve a system of equations with the variables of the parametric surface and the parametric line (black). The goal is to calculate P (intersection with the surface) and, from there, the vector V1. The problem is that I always get zero as the solution for all the variables.
Any help would be greatly appreciated! Thanks.question_surface_.mw

single PDE solver error ...

Asked by: sarah_r21 5

January 26 2025

1 2

Dear all,

I'm a new maple user trying to solve a single PDE in maple using finite volume.

For simplicity I'm using three volumes. When I'm trying to apply a simple flux limiter, up-wind scheme, (relation between the wall and the node values u[j+0.5](t)=u[j](t)), I'm solver works well and produces accurate results.

However, when I try to a more complicated flux limiter, the solver doesn't initialize and I'm getting an error:
"Error, (in dsolve/numeric/DAE/make_proc) specified dependent variables [u[0](t), u[.5](t), u[1](t), u[1.5](t), u[2](t), u[2.5](t), u[3](t), u[3.5](t), u[4](t)] do not agree with input system {u[0], u[1], u[2], u[3], u[4], u[1/2], u[1.5], u[2.5], u[3.5]}, differences: {u[1/2]}, {u[.5]}".

I would greatly appreciate it if somebody helps me on in this issue.

error.mw

How can fix `[Length of output exceeds limit of 10...

Asked by: salim-barzani 950

January 26 2025

1 4

in a lot of my equation i have such problem and really i don't know how fix this also i try to put : in end and sometime is work and i keep contionues but sometime not there is any way for solve this problem?

limit.mw

How can define this series for generate a functio...

Asked by: salim-barzani 950

January 26 2025

1 5

i don't know how generate this series and when i have a lot series which i can't make them automatically i don't know how write and replacing some structure like mu is zero or 1 as shown in picture can any one give me a hand?

both of them are same with little different

Is there some way to avoid this behaviour?...

Asked by: mmcdara 7601

January 25 2025

0 2

Let us suppose I open Maple, write a worksheet, save it in a folder A and then quit Maple.

Now I run a new session by double clicking on some mw file located in folder B, let us say //B/test_1.mw.
Once opened I do some modifications and decide to save this worksheet into a new file, let us say test_2.mw in the same folder B test_1.mw belongs to (which means I use Save As from the menu bar)

I'm regularly fooled by the fact that the default folder is not B, but the folder A I used in the previous session.

I find this very unpleasant.
Is this a Maple (2015) issue or something related to my operating system (Mac OSX Catalina)?
In case it is a Maple issue which is still present in more recent Maple versions, Would it be possible to set the default backup folder to be the folder to which the active worksheet belongs?

Thanks in advance

How remove this Error, (in Utilities:-RecognizeCyc...

Asked by: salim-barzani 950

January 25 2025

1 4

i need find parameter in explicite way without Rootof() so i need use code of explicite but i get error but when i use all parameter without explicite all parameter come out so why i get this error?

zero.mw

Customized Key Bindings?...

Asked by: studentX369 30

January 25 2025

2 6

It's 2024 and this is still something that doesn't exist? I'd just like to swap the Enter/Shfit+Enter behaviors since I find myself writing a lot of multi-line and custom procs and boy howdy it'd be nice if I could make Maple behave at least the littllest bit like, I dunno, every other product I own and use.

NODEMaple v1.1.0 released

by: Anthrazit 880 Product: Maple 2024

January 25 2025

0 1

Just around a month after the first release I am glad to announce the second public release of this project.

Changes from last release:

added angled cuts to beam ends
fixed bug for bolt connections with thick steel plates
rewrite check if fasteners are placed within beams
removed some obsolete procedures in NODEFunctions
minor changes in XML file headers

For more information see https://github.com/Anthrazit68/NODEMaple.

Why my out come is different by same method and sa...

Asked by: salim-barzani 950

January 25 2025

0 0

i found solution of PDE but there is some different from my solution and paper solution so there is must be a mistake becuase he solved by maple too he mentioned in the paper i try to figure out but i can't see any mistake from my solution can anyone watch where i did mistake, i change some letter in finding parameter but they are same like p=k&h=A&n=p&w=n

here is paper solution

parameter-different.mw

`How to calculate u = `((∂)/(∂ t...

Asked by: FZ 30

January 25 2025

1 10

`How to calculate u = `((&PartialD;)/(&PartialD; t) - (&PartialD;)/(&PartialD; x))^(-1)(z)?

>

restart;

>	with(PDEtools):

>	alias(z=z(x,y,t), u=u(x,y,t))

(1)

>

z := 32*delta2^3*(exp((2*a*y*delta2^3 + 2*(x + y + t)^3*(B1 + 2*B2)*delta2^2 + (2*a*delta1^2*y + t)*delta2 + 2*delta1^2*(x + y + t)^3*(B1 + 2*B2))/(delta1^2 + delta2^2)) - exp((-2*a*y*delta2^3 + 4*(B1 + B2/2)*(x + y + t)^3*delta2^2 + (-2*a*delta1^2*y - t)*delta2 + 4*delta1^2*(B1 + B2/2)*(x + y + t)^3)/(delta1^2 + delta2^2)))*a/((delta1^2 + delta2^2)^2*(exp((2*(delta1^2 + delta2^2)*(x + y + t)^3*B2 + 2*delta2*(a*(delta1^2 + delta2^2)*y + t/2))/(delta1^2 + delta2^2)) + exp((2*(delta1^2 + delta2^2)*(x + y + t)^3*B1 - 2*delta2*(a*(delta1^2 + delta2^2)*y + t/2))/(delta1^2 + delta2^2)))^3);

(2)

>

NULL

Download integ.mw

How do i plot the midpoint and distance?...

Asked by: paulmcquad 75

January 24 2025

1 3

I was trying to look for an easy way to plot the locations of the distance and midpoint on a graph. I found how to get the distance and midpoint functions but plotting them is hard.

Thanks in advance.