Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

Hi every body,

I have a function "p(v,T)" which I evaluated its critical point. after calculating when I want to plot diagram of "p-v" for some values of "T" around critical value of "T" I expect the shape of diagram for "T" bigger and smaller than critical value of "T" be different. but it not happened. Are here anyone can help me? The function "p(v,T)" is in the file. if you want calculate critical point and check I am right or wrong. Thanks criticalpoint.mw

is it possible to change ODE to PDE?

the ODE has diff(a(t),t) and diff(b(t),t)

how to convert to diff(t, a), diff(t, b) ?

I am trying to evaluate the following triple integral but it takes much time so i kill the job.


 

restart; R := 5; KK := proc (theta) options operator, arrow; evalf(int(int(int(1/(R*sin(theta)^2+(R*cos(theta)+Z)^2+(2*R*k.sin(theta))*cos(p))^2, p = 0 .. 2*Pi), Z = 0 .. 60), k = 1 .. 10, numeric)) end proc; evalf(KK((1/6)*Pi))

Warning,  computation interrupted

 

``


 

Download int_maple_prime2.mw

with(DEtools, buildsym, equinv, symtest):
ans := dsolve([eq2,eq3,eq4], Lie);
Error, (in dsolve) too many arguments; some or all of the following are wrong: [{a(t), b(t), c(t)}, Lie]
 
ans := dsolve([eq2+eq3+eq4 = exp(t)], Lie);
Error, (in PDEtools/sdsolve) too many arguments; some or all of the following are wrong: [{a(t), b(t), c(t)}, Lie]
 
ans := dsolve([eq2,eq3,eq4]);
sym2 := buildsym(ans);
Error, (in buildsym) invalid input: `ODEtools/buildsym` expects its 1st argument, sol, to be of type {algebraic, algebraic = algebraic}, but received [{c(t) = ...}, {b(t) = ...}, {a(t) = ...)}]
 
 
PDEtools[declare](a(t), b(t), c(t), prime = t):
symgen(eq2+eq3+eq4=0);
                       a(t) will now be displayed as a
                       b(t) will now be displayed as b
                       c(t) will now be displayed as c
   derivatives with respect to t of functions of one variable will now be
      displayed with 'symgen(....)'
 
 
update
if it can not do for 3 function a(t),b(t),c(t) system of differential equations
then
 
i change to use
eq2 := subs(b(t)=a(t),subs(c(t)=a(t),eq2));
eq3 := subs(b(t)=a(t),subs(c(t)=a(t),eq3));
eq4 := subs(b(t)=a(t),subs(c(t)=a(t),eq4));
 
with(DEtools, buildsym, equinv, symtest):
ans := dsolve(eq2 = 0, Lie);
buildsym(ans[1], a(t));
buildsym(ans[2], a(t));
buildsym(ans[3], a(t));
 
there are 3 answers, can i use one of it to recover the equation eq2 or  eq3 or eq4?
 
ans := dsolve(eq3=0, Lie);
buildsym(ans[1], a(t));
sym2 := buildsym(ans[2], a(t));
buildsym(ans[3], a(t));

sym := [_xi=rhs(sym2[2]),_eta=rhs(sym2[1])];
ODE := equinv(sym, a(t));
eq3 - ODE;
sym := [_xi=rhs(sym2[1]),_eta=rhs(sym2[2])];
ODE := equinv(sym, a(t));
eq3 - ODE;
but ODE is not equal to original eq3
ans := dsolve(eq4=0, Lie);
buildsym(ans[1], a(t));
buildsym(ans[2], a(t));
 
ans := dsolve(eq2+eq3+eq4=0, Lie);
sym := buildsym(ans[1], a(t));
ODE := equinv(sym, a(t));
eq2+eq3+eq4 - ODE;
sym := buildsym(ans[2], a(t));
ODE := equinv(sym, a(t));
eq2+eq3+eq4 - ODE;
sym := buildsym(ans[3], a(t));
ODE := equinv(sym, a(t));
simplify(eq2+eq3+eq4 - - ODE);
 
can not recover the original result

UPDATE

Thanks for checking. I verify I get the error and made screen shots below

When I add the convert() command, the error goes away. Here is screen shot

 

I am using Maple 2017, student version, on windows 7, 64 bit, home edition.

 

Original post

This is using Maple 2017 on windows.

With the following input, Maple pdsolve gives an error

pde:=diff(u(x,t),t)=k*diff(u(x,t),x$2);
bc:=D[1](u)(0,t)=0,D[1](u)(L,t)=0:
assume(L>0):
ic:=u(x,0)=piecewise(0<x and x<=L/2,0,L/2<x and x<L,1):
sol:=pdsolve([pde,bc,ic],u(x,t)):

However, if I add one line to convert the piecewise function above to piecewise, then pdsolve no longer gives an error. So the following input works

restart;
pde:=diff(u(x,t),t)=k*diff(u(x,t),x$2);
bc:=D[1](u)(0,t)=0,D[1](u)(L,t)=0:
assume(L>0):
ic:=u(x,0)=piecewise(0<x and x<=L/2,0,L/2<x and x<L,1):
ic:=convert(ic,piecewise,x):
sol:=pdsolve([pde,bc,ic],u(x,t)):

 

Notice the extra line. Why does one have to convert piecewise to piecewise to make pdsolve accept the input?

sorry did not write down the error message and I am writing this from school library PC. But if you try the first case, you'll see the error.

 

I have final project to make a media for learning mathematic using maple. But I'm so confused to make a net of cuboid, anybody can help me? please :D

Hi,

 

I have a problem of having a problem to solve the following equation with the this error. I found out that it might be due to that I have a differential that is squared and maple could not calculate it as after square root it will have positive and negative. May I know how to overcome this other than changing my equations?

ODE_summarize.mw
 

restart; with(DEtools)

````

sol1 := alpha*(diff(f(y), y, y, y)) = -(1/4)*f(y)*(diff(f(y), y, y))*n+(1/2)*(diff(f(y), y))^2*n-(3/4)*f(y)*(diff(f(y), y, y))+(1/2)*(diff(f(y), y))^2-g(y), diff(g(y), y, y) = -(1/4)*P[r](f(y)*(diff(g(y), y))*n-4*n*(diff(f(y), y))*g(y)+3*f(y)*(diff(g(y), y)))

alpha*(diff(diff(diff(f(y), y), y), y)) = -(1/4)*f(y)*(diff(diff(f(y), y), y))*n+(1/2)*(diff(f(y), y))^2*n-(3/4)*f(y)*(diff(diff(f(y), y), y))+(1/2)*(diff(f(y), y))^2-g(y), diff(diff(g(y), y), y) = -(1/4)*P[r](f(y)*(diff(g(y), y))*n-4*n*(diff(f(y), y))*g(y)+3*f(y)*(diff(g(y), y)))

(1)

bc := (D(f))(y)

(D(f))(y)

(2)

gg := convert(bc, diff)

diff(f(y), y)

(3)

gg1 := limit(gg, y = infinity)

limit(diff(f(y), y), y = infinity)

(4)

gg2 := convert(gg1, D) = 0

limit((D(f))(y), y = infinity) = 0

(5)

gg2

(D(f))(y) = 0

(6)

bc1 := eval(f(y), y = 0) = 0, eval((D(f))(y), y = 0) = 0, convert(gg1, D) = 0, limit(g(y), y = infinity) = 0, eval(g(y), y = 0) = 1

f(0) = 0, (D(f))(0) = 0, limit((D(f))(y), y = infinity) = 0, limit(g(y), y = infinity) = 0, g(0) = 1

(7)

``

odesub1 := eval(eval(sol1, n = .6), P[r] = 0)

alpha*(diff(diff(diff(f(y), y), y), y)) = -.9000000000*f(y)*(diff(diff(f(y), y), y))+.8000000000*(diff(f(y), y))^2-g(y), diff(diff(g(y), y), y) = 0

(8)

sol2 := dsolve({bc1, odesub1}, numeric, [f(y), g(y)], output = operator, continuation = alpha, initmesh = 2400, method = bvp[midrich])

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

``


 

 

 

 

 

 

 

 

 

 

I have the following expression

((4*(N-i+2))*((N-i-2)*(-(N-i-4)*(N+i+2)*(N+2)*(N+4)+N^4+4*N^3+4*N^2+16*N-40)-(4*(N-1))*(2*N+3)*(N+5))+(8*(N+5))*(N^2+8*N+6))/((N-i+1)*(N-i+3)*((N-i-2)*(i+3)*(N+2)*(N+4)-(8*(N+5))*(N-1)))

The parameters i and N are nonnegative integers and i is less than or equal to N. The purpose is to make it as short as possible. Based on my experience, it could be expressed as a small binomial expression or as a sum of two or three binomials. However, by Maple commands the conversion does not give me binomials or any smaller expression.

Is there any way for the conversion to binomials or any other conversion to shorten the expression?

I appreciate any help.

i want to solve this DAE system usin Dsolve , but i obtain this error message (cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up), if anyone can help me ,

I am trying to export a number of matrices from maple to matlab with meaningful names.

For instance with this code:
legend := ["ini_que", "ini_que_A", "ini_que_B"];
ExportMatrix("test.mat", [r_mean_Q_ini, r_mean_Q_ini_A, r_mean_Q_ini_B], arraynames = legend, target = MATLAB);

The problem is when I open the resulting file in either python or matlab, I only get  the matrices with names "ini_que" and "ini_que_". My guess is that  long strings in arraynames are truncated and only one of the options are kept.

Is this the case and can the maximum length of the name of the matrix be changed? Or is the only way to use shorter but less readable names?

Dear all

I have an operator given below in the image. I want expand this operator upto order 5, when there are three independent variables x, y, t(i=1,2,3). The expansion can also be obtained manually, but that is always prone mistake, is the expansion posible using any routine of Differential Geometry package?

I have installed maple in my 64 bit linux and on running calculation a window pop up saying kernel connection not available. I have disabled my firewall still the problem persist. The window freezes on clicking menu. Thankz in advance.

Hi guys ,

Actually i dont know how to solve the following complicated differential equations by numerical methods ,

numerical.mw

 

Thank you for your attention to this matter

Maple 16 code

 

N1 := FileTools[Text][CountLines](g)

I encounter an error message

in FileTools:-Text:-CountLines) permission denied

What  went wrong ?  This never happened before

I  re install  Maple 16, the same error persists.

 

Please help

Martin
 

That the Bernoulli numbers has z/(exp(z)-1)) as an exponentional generating functions is of course very well known. I am wondering why the gfun package doesn't seem to be able to work this out? Naive approaches like

gfun[guessgf]([seq(bernoulli(n),n=0..100)],z);

give FAIL. I would expect gfun to be able to transform the given sequence corresponding to replacing A(z) by 1/A(z), easily recognize (exp(z)-1))/z, and transform back. Perhaps the package is in need of maintenance?

Any help would be much appreciated.

Best,

Soren

 

 

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