Advanced Search

Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022
View all posts
Maple 2022 Questions and Posts Feed

Show steps for viscous Burger's equation...

Asked by: 130
solve
March 11 2025
0  2

Hi!

I am studying Burger's equation, and I would like to see the steps that Maple takes to solve this.  "ShowSteps" doesn't seem to work.

Unfortunately, I am unable to share the worksheet I made.

Server Error - MaplePrimes

 
 

MaplePrimes
 
Advanced Search
 
 
Connect with Maplesoft:
Questions  |  Posts  |  Tags  |  Users  |  Unanswered  |  Maplesoft Blog  |  Badges  |  Recent
About  |  MaplePrimes Help  |  Support
© Maplesoft, a division of Waterloo Maple Inc. .  |  maplesoft.com  |  Terms of Use  |  Privacy  |  Consent Preferences  | Trademarks

 

loading

Error occurred during PDF generation. Please refresh the page and try again

E-Mail Address:
 
Password:
 
Remember Me:
Automatically sign in on future visits
 
 
Forgot your password?
Create a New Account
 

Reduced Involutive Form...

Asked by: dds 20
pde differential-equations rifsimp
February 13 2025
2  8

Dear Maple Community,

I come to you with a question about the reduced involutive form (rif) package. Namely, I decided to try the classic example from the "LONG GUIDE TO THE STANDARD FORM PACKAGE", which dates back to 1993. Here is the link to the complete documentation:

https://wayback.cecm.sfu.ca/~wittkopf/files/standard_manual.txt

So, the example is the following:

2.1 SIMPLE EXAMPLES

EXAMPLE A

Consider the system of nonlinear PDEs:       

y Zxxx - x Zxyy  =  Zyy - y Zy

                        2     2    2
2 y x Zxxx Zxyy + x Zxxx + x y Zxyy  =  0

                  2    2
y Zxyy - x W + 2 x  y Z  =  0

                 2    2
Zyy - y Zy  + 2 x  y W  =  x W

where the dependent variables W and Z are functions of the
independent variables x and y, and Zxxx denotes the third partial
derivative of Z with respect to x etc.

After making computations back in 1993 with Maple V, they obtain the following involutive form:

In our original notation the (considerably) simplified system is:
                                            2
  Zxxx = 0, Zxy = 0, Zyy = y Zy, W = 2 x y Z

So, I tried the same system of PDEs in the modern Maple and the modern rifsimp() command. You can find the result below:

I demo_question.mw

The problem is that nowadays [Maple 2022.1] , I get only the trivial solution: z = 0 and w = 0.

Could someone clarify, please, where the truth is and what am I doing wrong?

Thanks a lot in advance for any help and clarification!

Best regards,

Dr. Denys D.
 

> 

restart:
> 

with(DETools):
> 

PDE1 := y*diff(z(x,y), x$3) - x*diff(z(x,y),x,y$2) = diff(z(x,y),y$2) - y*diff(z(x,y), y);

y*(diff(diff(diff(z(x, y), x), x), x))-x*(diff(diff(diff(z(x, y), x), y), y)) = diff(diff(z(x, y), y), y)-y*(diff(z(x, y), y))

 (1)
> 

PDE2 := 2*x*y*diff(z(x,y),x$3)*diff(z(x,y),x,y$2) + x*(diff(z(x,y),x$3))^2 + x*y^2*(diff(z(x,y),x,y$2))^2 = 0;

2*x*y*(diff(diff(diff(z(x, y), x), x), x))*(diff(diff(diff(z(x, y), x), y), y))+x*(diff(diff(diff(z(x, y), x), x), x))^2+x*y^2*(diff(diff(diff(z(x, y), x), y), y))^2 = 0

 (2)
> 

PDE3 := y*diff(z(x,y),x,y$2) - x*w(x,y) + 2*x^2*y*z(x,y)^2 = 0;

y*(diff(diff(diff(z(x, y), x), y), y))-x*w(x, y)+2*x^2*y*z(x, y)^2 = 0

 (3)
> 

PDE4 := diff(z(x,y), y$2) - y*diff(z(x,y),y) + 2*x^2*y*w(x,y)^2 = x*w(x,y);

diff(diff(z(x, y), y), y)-y*(diff(z(x, y), y))+2*x^2*y*w(x, y)^2 = x*w(x, y)

 (4)
> 

sys := [PDE1, PDE2, PDE3, PDE4]:
> 

rif := rifsimp(sys, [[w], [z]], indep = [x,y]);

table( [( Case ) = [[z(x, y)*(8*z(x, y)^2*y^2*x^2-1) = 0, diff(z(x, y), x), "false split"]], ( Solved ) = [w(x, y) = 0, z(x, y) = 0] ] )

 (5)
 

 

How to integrate it?...

Asked by: Ahmed111 130
integration differential-equations
February 03 2025
0  2

How to integrate eq (4)? Since 'a', 'b', and 'c' are constant. 

> 

restart
> 

with(DEtools)
> 

declare(z(x), y(x))

declare(z(x), y(x))

 (1)
> 

eq1 := (1/2)*(-z(x)^3-2*c*z(x))*(diff(diff(y(x), x), x))-((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x)) = 0

(1/2)*(-z(x)^3-2*c*z(x))*(diff(diff(y(x), x), x))-((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x)) = 0

 (2)
> 

eq2 := simplify(z(x)*eq1)

-z(x)*(z(x)*((1/2)*z(x)^2+c)*(diff(diff(y(x), x), x))+((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x))) = 0

 (3)
> 

eq3 := eval(int(lhs(eq2), x))

int(-z(x)*(z(x)*((1/2)*z(x)^2+c)*(diff(diff(y(x), x), x))+((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x))), x)

 (4)

NULL

Download integration.mw

How to simplify Eqs. (3), (5) and (6) and write in...

Asked by: FZ 30
differentiation substitution pde
January 31 2025
0  5
> 

restart; with(PDEtools); declare(F(x, t), G(x, t), H(x, t))

F(x, t)*`will now be displayed as`*F

  

G(x, t)*`will now be displayed as`*G

  

H(x, t)*`will now be displayed as`*H

 (1)
> 

q := 1-(diff(diff(log(F(x, t)), x), t)); r := G/F; s := H/F

1-(diff(diff(F(x, t), t), x))/F(x, t)+(diff(F(x, t), x))*(diff(F(x, t), t))/F(x, t)^2

  

G/F

  

H/F

 (2)
> 

r1s1 := r*s; r1s1der := diff(r1s1(x, t), x)
> 

qt := diff(q(x, t), t)
> 

eq1B := F(x, t)^3*(qt+r1s1der) = 0; eq12B := simplify(expand(eq1B))

-F(x, t)^3*(diff((diff(diff(F(x, t), t), x))(x, t), t))/(F(x, t))(x, t)+F(x, t)^3*(diff(diff(F(x, t), t), x))(x, t)*(diff((F(x, t))(x, t), t))/(F(x, t))(x, t)^2+F(x, t)^3*(diff((diff(F(x, t), x))(x, t), t))*(diff(F(x, t), t))(x, t)/(F(x, t))(x, t)^2-2*F(x, t)^3*(diff(F(x, t), x))(x, t)*(diff(F(x, t), t))(x, t)*(diff((F(x, t))(x, t), t))/(F(x, t))(x, t)^3+F(x, t)^3*(diff(F(x, t), x))(x, t)*(diff((diff(F(x, t), t))(x, t), t))/(F(x, t))(x, t)^2+F(x, t)*(diff(G(x, t), x))*H(x, t)-2*G(x, t)*H(x, t)*(diff(F(x, t), x))+F(x, t)*G(x, t)*(diff(H(x, t), x)) = 0

 (3)
> 

D_x_x_G_F := (diff(G(x, t), x, x))*F(x, t)-2*(diff(G(x, t), x))*(diff(F(x, t), x))+G(x, t)*(diff(F(x, t), x, x)); D_t_t_F_F := F(x, t)*(diff(F(x, t), `$`(t, 2)))-2*(diff(F(x, t), t))^2

(diff(diff(G(x, t), x), x))*F(x, t)-2*(diff(G(x, t), x))*(diff(F(x, t), x))+G(x, t)*(diff(diff(F(x, t), x), x))

  

F(x, t)*(diff(diff(F(x, t), t), t))-2*(diff(F(x, t), t))^2

 (4)
> 

NULL
> 

rxt := diff(diff(r(x, t), x), t)
> 

eq2B := -2*q*r+rxt = 0
> 

eq22B := simplify(expand(eq2B))

((-F*F(x, t)*G(x, t)+2*G*F(x, t)^2)*(diff(diff(F(x, t), t), x))+(diff(diff(G(x, t), t), x))*F*F(x, t)^2+((2*F*G(x, t)-2*G*F(x, t))*(diff(F(x, t), x))-F*(diff(G(x, t), x))*F(x, t))*(diff(F(x, t), t))-(diff(G(x, t), t))*(diff(F(x, t), x))*F*F(x, t)-2*G*F(x, t)^3)/(F*F(x, t)^3) = 0

 (5)
> 

> 

sxt := diff(diff(s(x, t), x), t)
> 

eq3B := -2*q*s+sxt = 0
> 

eq32B := simplify(expand(eq3B))

((-F*F(x, t)*H(x, t)+2*H*F(x, t)^2)*(diff(diff(F(x, t), t), x))+(diff(diff(H(x, t), t), x))*F*F(x, t)^2+((2*F*H(x, t)-2*H*F(x, t))*(diff(F(x, t), x))-F*(diff(H(x, t), x))*F(x, t))*(diff(F(x, t), t))-(diff(H(x, t), t))*(diff(F(x, t), x))*F*F(x, t)-2*H*F(x, t)^3)/(F*F(x, t)^3) = 0

 (6)
> 

"#`# How to simplify Eqs. (3), (5) and (6) and write in terms of following bilineat operators` by using (4)"?""
> 

NULL

NULL

Download BE.mw

Custom file extensions ?...

Asked by: segfault 140
worksheet gui save
December 16 2024
0  0

Is it possible to configure newer maple versions to use a different file extension ?

I have a lot of  Maple 9 files  with .mw extension. I dont want them opened and saved by a later version as they are valuable and actually work better than later maple versions which throws unneccesary signum errors. The results are verified so the signum errors are bogus in the recent maple versions running the same file.

Particularly, can I configure e.g. Maple 2022 to save to a different file extension say .mww or similar rather than .mw so I can avoid destroying to original 9.5 files?

Issues with Variational Derivative and Commutator...

Asked by: WA573 80
calculus-of-variations commutator lagrangian
November 01 2024
0  4

I’m working on deriving the equation of motion (16) from equation (9) (see attached image), but I’ve encountered a couple of issues in Maple. i) The variational derivative of Lagrangian, and ii) the commutator is zero, which isn’t expected.

How do we fix these issues? Are there any specific packages regarding the construction of Lagrangian?

VariationDerivative.mw

Why does Maple interpret 1 .05 as 1 * 5. Note t...

Asked by: max125 195
multiplication syntax
October 12 2024
3  4

I can't understand why Maple interprets 1 .05  as 1 * 5 = 5 , and 2 .05  as 2 * 5 = 10 . Note the space between 1 and .05
In a different calculation I accidentally inserted a space between 1 and .05, and received a strange answer, and finally narrowed it down to a space.
But now I wonder why it is it is interpreting this way. Also I see that 2  0.05 produces an error. But  2 .05 is treated as 10. There is an implied multiplication? But the multiplication should be 2 * .05 , which is 1 and not 10.

need assistance in finding a way...

Asked by: mz6687 40
substitution homework simplification
October 11 2024
0  6

I have encountered an issue: eq1 is not satisfied, though eq2 is satisfied for the parametric value (10). I need assistance in finding a way to ensure that both equations are satisfied simultaneously. Please provide guidance or suggest a potential approach for addressing this issue.verf_kk.mw

How to produce Mathematica file into Maple...

Asked by: AHSAN 155
mathematica pdf import
September 29 2024
0  4

Could anyone help me to convert a code written in Mathematica to a Maple worksheet? I have PDF only. Could any one have a look on Mpale sheet and PDF....

Mathematica__to_Maple.mw

Mathematica_file.pdf

Problems saving a worksheet as task...

Asked by: Jno 45
task helptools windows11
September 20 2024
0  0

Hi,

I recently moved from Windows 10 to Windows 11. I am using Maple 2022.2, and I got that installed and working OK. 

I have four Maple worksheets that I have saved as tasks on Windows 10, but my OS move requires some adjustments. When I try save the modified worksheets to the default Maple help database, I get an error saying that the database is read-only. When I try to make a new database file, Maple asks if it should create it, but then I get an error that Maple can't open the new database.

Suggestions?

Thanks,

Jno.

Can someone help me open this file?...

Asked by: Krag 5
document corruption backup
September 04 2024
1  1

So I have this Maple document that I worked on yesterday, and now when I open it it just opens as the start-up screen where I can choose between document and worksheet mode. I can see that the file is much larger (900 kb) than an empty document, so it should definitely have the data still in there, but opening it with a text editor I couldn't manage to fix my issue. Does anyone have any tips? I have a back-up of the file (from the restore backup menu), but most of the content is not there, so it would be very helpful to get this one fixed.

Exercises.mw
Thanks in advance, 
Kristian.

Explore a surface...

Asked by: Sotto 60
explore plotting
July 15 2024
0  1

Dear all,

I'd like to explore graphically a polynomial surface depending on two parameters a and b.

The problem is that, as soon as I start playing with the sliders, Maple freezes and I have to 'force quit'.

Can you please tell me if you have the same problem with this example?

Thanks.

> 

restart:
> 

with(plots):
> 

K := 1 - y*x - (1 - x)*(b*x^3 + a*x^2 + x + 1)*(1 - y)*(b*y^3 + a*y^2 + y + 1)

1-y*x-(1-x)*(b*x^3+a*x^2+x+1)*(1-y)*(b*y^3+a*y^2+y+1)

 (1)
> 

Explore(plot3d(K, x=0..1, y=0..1,  font= [Times, bold, 20], labels= ['x', 'y','z'],   labelfont= [Times, bold, 40],  title = "K(x,y)"), b = 0..1., a=0..1.);
 

 

Download Explore.mw

non-linear system...

Asked by: Jose Carrero 10
rootfinding fsolve numeric
June 30 2024
2  2

I have this problem with this system of equations, when I solve the 13x13 system it does not give me any solution, neither giving seed values ​​nor placing full digits. The exercise is solved and I tried to assume close values ​​and it doesn't work for me, it leaves everything expressed with the fsolve command.

Download p1.mw

How does Maple solve, int(y'(x)*f(x), x) =[int(sqr...

Asked by: Joseph Poveromo 25
ode dsolve differential-equations
June 21 2024
0  8

'odeadvisor' suggests isolating y(x) from the equation as a first step, y=G(x,y'(x)), then apply the method of 'patterns'. For the first step, y(x) = (9/4)*[(y'(x))^2]/{[int(f(x),x)]^5} is what I found but, could take it no further. Nevertheless, Maple finds an intrinsic solution of the form, (3/4)*y(x)^(4/3) +(2/3)*int(sqrt(y(x)*f(x))^(-5/3) + _C1 =0, from which an explicit solution can be obtained. If anyone can supply the steps leading to the Maple solution - that would be great.

How do I solve a system of differential equations ...

Asked by: spalinowy 30
ode dsolve numeric
June 19 2024
0  4

Hello everyone

I need help solving a system of equations as below. I'm looking for a way to do it, but I don't understand the general concept of how such an equation is calculated. So far I've been using a package in LabVIEW that worked similarly to Simulink and that was clear to me, whereas here I'm overwhelmed by the multitude of options and that's why I'm asking for help.

I need to solve these equations analogously to Matlab-Simulink, i.e., a time interval and integration step, and a numerical procedure in symbolic versions.

Help_me.mw

1 2 3 4 5 6 7 Last Page 1 of 42