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how i can dsolve this differential equations........

Asked by: 9009134 110
dsolve
August 14 2017
0  5

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

zah.mw
 

``

restart; L := 100; h := 1; eq1 := 1130*(diff(U(x), x, x))+1130*(diff(W(x), x))*(diff(W(x), x, x))+1130*(diff(U(x), x, x, x, x))

1130*(diff(diff(U(x), x), x))+1130*(diff(W(x), x))*(diff(diff(W(x), x), x))+1130*(diff(diff(diff(diff(U(x), x), x), x), x))

 (1)

eq2 := 1130*(diff(W(x), x))*(diff(U(x), x, x)+(diff(W(x), x))*(diff(W(x), x, x)))+(diff(W(x), x, x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(W(x), x, x, x, x, x, x))+(10405/6)*(diff(W(x), x, x, x, x))+10

1130*(diff(W(x), x))*(diff(diff(U(x), x), x)+(diff(W(x), x))*(diff(diff(W(x), x), x)))+(diff(diff(W(x), x), x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(diff(diff(diff(diff(diff(W(x), x), x), x), x), x), x))+(10405/6)*(diff(diff(diff(diff(W(x), x), x), x), x))+10

 (2)

eq3 := diff(varphi(z), z, z)-.35*(diff(W(x), x, x))

diff(diff(varphi(z), z), z)-.35*(diff(diff(W(x), x), x))

 (3)

dsys3 := {eq1, eq2, eq3, U(0) = 0, U(L) = 0, W(0) = 0, W(L) = 0, `ϕ`(-(1/2)*h) = 0, `ϕ`(-(1/2)*h) = 2, ((D@@1)(W))(0) = 0, ((D@@1)(W))(L) = 0, ((D@@2)(W))(0) = 0, ((D@@2)(W))(L) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {x, z}

  

``


 

Download zah.mw

 

fix error and identify any other wrong and explain...

Asked by: bashar27 55
August 14 2017
0  1

> {w = -4*mu, a[-1] = -12*mu/(a+b), a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0, b[1] = 0};
  /                     12 mu                                              
 { w = -4 mu, a[-1] = - -----, a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0,
  \                     a + b                                              

           \
   b[1] = 0 }
           /
> restart;
>
> w := -4*mu;
                                    -4 mu
> a[-1] := -12*mu/(a+b);
                                     12 mu
                                   - -----
                                     a + b
> a[0] := a[0];
                                    a[0]
> a[1] := 0;
                                      0
> b[-1] := 0;
                                      0
> b[0] := 0;
                                      0
> b[1] := 0;
                                      0
> xi := x+w*t;
                                 x - 4 mu t
> P := sqrt(mu)*tan(A-sqrt(mu)*xi);
                      (1/2)    /      (1/2)             \
                    mu      tan\A - mu      (x - 4 mu t)/
> u := a[0]+a[1]*P/(1+lambda*P)+a[-1]*(1+lambda*P)/P+b[0]*sqrt(sigma*(1+P^2/mu))/P+b[1]*sqrt(sigma*(1+P^2/mu))+b[-1]*sqrt(sigma*(1+P^2/mu))/P^2;
                (1/2) /             (1/2)    /      (1/2)             \\
           12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
    a[0] - -------------------------------------------------------------
                                  /      (1/2)             \            
                       (a + b) tan\A - mu      (x - 4 mu t)/            
> Diff(u, x, t)+a*(Diff(u, x))*(Diff(u, x, y))+b*(Diff(u, `$`(x, 2)))*(Diff(u, y))+Diff(u, `$`(x, 3), y);
/   2   /            (1/2) /             (1/2)    /      (1/2)             \\\
|  d    |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|
|------ |a[0] - -------------------------------------------------------------|
| dt dx |                              /      (1/2)             \            |
\       \                   (a + b) tan\A - mu      (x - 4 mu t)/            /

  \     /    /    
  |     | d  |    
  | + a |--- |a[0]
  |     | dx |    
  /     \    \    

          (1/2) /             (1/2)    /      (1/2)             \\\\ /   2   /
     12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |  d    |
   - -------------------------------------------------------------|| |------ |
                            /      (1/2)             \            || | dy dx |
                 (a + b) tan\A - mu      (x - 4 mu t)/            // \       \

              (1/2) /             (1/2)    /      (1/2)             \\\\     /
         12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||     |
  a[0] - -------------------------------------------------------------|| + b |
                                /      (1/2)             \            ||     |
                     (a + b) tan\A - mu      (x - 4 mu t)/            //     \

   2 /            (1/2) /             (1/2)    /      (1/2)             \\\\ /
  d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |
  -- |a[0] - -------------------------------------------------------------|| |
     |                              /      (1/2)             \            || |
     \                   (a + b) tan\A - mu      (x - 4 mu t)/            // \

      /            (1/2) /             (1/2)    /      (1/2)             \\\\
   d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||
  --- |a[0] - -------------------------------------------------------------||
   dy |                              /      (1/2)             \            ||
      \                   (a + b) tan\A - mu      (x - 4 mu t)/            //

     / 4 /            (1/2) /             (1/2)    /      (1/2)             \\
     |d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
   + |-- |a[0] - -------------------------------------------------------------
     |   |                              /      (1/2)             \            
     \   \                   (a + b) tan\A - mu      (x - 4 mu t)/            

  \\
  ||
  ||
  ||
  //
> value(%);
                       /                                 2\
              3        |       /      (1/2)             \ |
         96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /
         --------------------------------------------------
                               a + b                       

                                                                2   
                            /                                 2\    
                   3        |       /      (1/2)             \ |    
              96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /    
            - --------------------------------------------------- +
                                                         2          
                               /      (1/2)             \           
                    (a + b) tan\A - mu      (x - 4 mu t)/           

                                                  /             
                                                  |             
                             1                    |     (5/2) /
           -------------------------------------- \96 mu      \1
                                                3               
                      /      (1/2)             \                
           (a + b) tan\A - mu      (x - 4 mu t)/                

                       (1/2)    /      (1/2)             \\
            + lambda mu      tan\A - mu      (x - 4 mu t)//

                                               2\   
           /                                 2\ |   
           |       /      (1/2)             \ | |   
           \1 + tan\A - mu      (x - 4 mu t)/ / / -

                                                 /             
                             1                   |     (5/2) /
           ------------------------------------- \96 mu      \1
                      /      (1/2)             \               
           (a + b) tan\A - mu      (x - 4 mu t)/               

                                                            /
                       (1/2)    /      (1/2)             \\ |
            + lambda mu      tan\A - mu      (x - 4 mu t)// \1

                                           2\\
                 /      (1/2)             \ ||
            + tan\A - mu      (x - 4 mu t)/ //
> simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion
>

 

plot an indefinite integral ...

Asked by: mehdi jafari 774
plot integral integration
August 14 2017
0  7

hi every one, i want to plot an indefinite integral  , it is some what complex and maple can not compute the answer, ( but numeric integration can be computed) , but we want to plot the output, what should we do ? tnx for help in advance

corrected.mw

weighted norm of an expression...

Asked by: mehdi jafari 774
August 14 2017
0  3

how can we compute wighted norm of a matrix or a vector in maple? 

How can I convert a result to a trigonometric iden...

Asked by: Gillee 237
trigonometric-identities convert tanh
August 13 2017
1  5

``

How can I convert the result (2) to equal to the trigonometric identity (kw/s^2)*tanh(a*s/2)?

``

> 

g := kw*piecewise(t < a, t, t < 2*a, 2*a-t)

kw*piecewise(t < a, t, t < 2*a, 2*a-t)

 (1)
> 

simplify((int(exp(-s*t)*g, t = 0 .. a)+int(exp(-s*t)*g, t = a .. 2*a))/(1-exp(-2*a*s)))

-(exp(-a*s)-1)*kw/((exp(-a*s)+1)*s^2)

 (2)
> 

``

Download trigonometric_id.mw

 

how to dsolve for this equation?...

Asked by: LeeHoYeung 535
August 13 2017
0  5

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)
 

how to find the contour of time series data? and c...

Asked by: LeeHoYeung 535
curvature contour
August 12 2017
0  1

how to find the contour of time series data? and how to find curvature function of this contour?

search value plot maximize...

Asked by: lucaud 45
August 12 2017
0  1

In this fuction the maximize is about at t=46 and x=46 but in the plot I look other max at other value, why?because is discontinus fuction?I need not the local max (it is potential energy but I think don't matter)optimization2enerpot.mws

how to solve this system?...

Asked by: LeeHoYeung 535
solve groebner
August 12 2017
0  0
updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
 
restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);
 
g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));
 
                                   1, c1
                               2       2    2   2
                           16 y  + 16 x , s1  s2
                                           2
                                 8 x, c1 s2
                                2      2    2  
                             2 y  + 2 x , s1  c2
                                 2 x, c1 c2
                            3            2        
                         2 x  - 2 x + 2 y  x, s2 c2
                                        2
                                   1, c2
                                   2 x, s3
                                    2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system
 
but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.
 
originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));
 

contours from an array of points using surfdata in...

Asked by: mikemeson 25
contour plotting surfdata
August 11 2017
2  5

I found from this forum that to plot a 2D array of points use can be made of the Maple procedure surfdata.
 

Does anyone have suggestions on how to plot contours in (preferrably) Maple 16 or Maple 17?

I tried the following

Output := Array(-10 .. 10, -10 .. 10, proc (i, j) options operator, arrow; i^2+j^2 end proc):
F := proc (x, y) -> x^2+y^2 end proc:
surfdata(Output, color = F, dimension = 2);

but "the option dimension = 2" is a Maple 18 addition.

Ideally, I would like also to be able to plot contours with options found in the procedure
contourplot

Is there a way to numerically solve a set of PDEs ...

Asked by: Dmitrii 15
numeric pdsolve
August 11 2017
1  8

Please illustrate the answer on the example of a simple wave equation, for instance.

Inverse Poisson Distribution...

Asked by: Teep 200
quantile probability poisson-distribution
August 11 2017
1  10

I'm wondering if there is an available command that can evaluate the number of terms required to produce a desired outcome.

Specifically, I am interested in determining the probability of a Poisson distribution, given the parameter (mean) value and the probability outcome. I can obtain the desired result using trial and error / brute force, but I am curious to know if there is a more efficient way. 

Suppose that, lambda = 2.6 and the cumulative sum of the probabilities is 95%. I know that I must add the first 6 terms for P(x) in the series (x=0,1, ..,5) to sum to 0.95. Each term ...  P(x=0)= 0.07, P(x=1)=0.19, and so on.

However, how can we know that desired 95% outcome can be determined from the first 5 terms without trial & error?

calculating a tensorial term ...

Asked by: trace 75
tensor metric
August 11 2017
0  1

Hi guys ,

i computed a tensorial term with respect to a metric and i think i made mistake !! what do you think ?

problem.mw

Best Regards

 

 

Issues with pdsolve...

Asked by: Bart 117
pdsolve
August 11 2017
4  6

will give me

which is indeed a solution of the PDE1

will give me

which is not a solution of the PDE2

However, both differential equations are equal, only the arguments are swapped around. Am I doing something wrong, or is this a bug?

Thanks

How should I save a procedure and read it into a ...

Asked by: Ronan 1341
August 10 2017
1  17

I have a module with quite a few procedures and it is getting too long and complex. Basicially I write each procedure in a seperate document, them copy and paste it into the module. I want to improve matters as save each proc and read it in to the module

e.g.  Qdim:=proc(A,B).........end proc

        save Qdim , "Qdim.?"   have tried .txt ,.mla , .m  They save fine.

in the module have tried

read "Qdim.txt" etc.   I have included Qdim in export but Qdim doesnt work Qdim(A,B) returns Qdim(A,B)

read "C:\Users\Ronan\Documents\MAPLE\Rational Trinonometry\Qdim.m";

which procuces an error

Error, (in unknown) could not open `C:UsersRonanDocumentsMAPLERational TrinonometryQdim.m` for reading

 

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