How to create animation f(x)=x^2, g(x)=sqrt(x), x=0, and x=1 if rotation about line y=-1 and x=-1?

Thank for your attention and helping.

Hello everybody,

I am trying to solve a partial differential equation (wave equation) with initial conditions that contain derivative and x-varying values

My equation
Uxx – Utt = 0 (hiperbólica) where xx and tt denote second partial derivatives with respect to x and t
0 <= x <= 10; t > 0;
u(0,t) = u(10,t) = 0;
Ut(x,0) = 0;
u(x,0)=
x for 0 <= x < 5
10-x for 5 <= x <= 10

I ve defined my equation as follow
> PDE := diff(u(x,t),x,x)=diff(u(x,t),t,t);

I m first trying without the x-varying initial condition.

> IBC := {u(0,t)=0,u(10,t)=0,u(x,0)=10-x,diff(u(x,0), t) = 0};
Returns the ugly

And that gives error when trying to solve
> pds := pdsolve(PDE,IBC,numeric);
Error, (in pdsolve/numeric/process_IBCs) initial/boundary condition does not contain the dependent variables of the PDE: 0 = 0

Another try with
> IBC := {u(0,t)=0,u(10,t)=0,u(x,0)=10-x,diff(u(x,t=0), t) = 0};

Looks like more promissing but returns (in a solving attempt)
> pds := pdsolve(PDE,IBC,numeric);

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions must depend upon exactly one of the independent variables: diff(u(x, t = 0), t) = 0

Regarding the x varying initial condition, I ve tried the `assuming` keyword in various attempts but without success.

Anybody could help on the matter?

Thanks in advance for anytip.
Have a good day
Nicolas

Hello those in Mapleprimes,

I want to obtain the result of the following codes,

shift:=(f::procedure)->(x->(f(x+1))):

shift(sin);

as x->sin(x+1)..................(1)

But, the result I could get was only

x -> f(x + 1)......................(2)

Please teach me how I can obtain the result as (1), not (2)?

Thanks in advance.

taro

Hello,

I have a easy question I think but blocking for me.

I have a expression g(t):=f(x(t),alpha(t),beta(t))

I give 

x(t):=0.12
alpha(t):=0
beta(t):=0

I would like to evaluate g(t).

And for the moment x(t), alpha(t) and beta(t) aren't replaced by their values.

How can i do in order to have the evaluation of g(t) ?

Thanks a lot for help.

i am using plot command to plot the first vs the second column in the attached file A.txt

it is giving a strange plot. while plotting the first vs second column in kgraph i am getting the correct plot

why is maple giving me a wrong plot 

you can find the two plots and the raw data file A.txt

Download A.txt

Dihedralgroup(9) acts on the set 1..9 and has order 9

g:=SmallGroup(18,1) acts on the set 1..18 and has order 18.

Question:

Is it possible to let g act on 1..9, too) and how can I do that?

Best regards

Kurt Ewald

Hallo,

Is there a fairly straightforward method for obtaining an array of coordinates from an implicit equation? I have an ellipse defined implicitly (by a horrendously involved expression) and can't figure out how to extract a set of coordinates from an implicitplot. I'm reluctant to use seq and fsolve with a fixed stepsize.

Would be grateful for some insight!

Thanks.

Weirp

Hi Mapleprimers,

I was wondering if there way a way to use restart(); and clear Maple's memory, but protect the memory in a certain variable?  I would like to return the memory to the operating system, but keep a symholic function in memory.

Alternatively, is there a way to save a symbolic function to a file, then reload it at a seperate time?

hi everyone,i have two questions,
1. i have a problem with select command? 

2. how i can select the parts which their addition of differential oreder,are the same ? for example,the second expression in eq[1] has the addition order of 2,third has 4 and ... how can isolate addition order ? tnx in advance . 

Download select.mw

Hi All. Hope all is well.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of polynomials of arbitrary form[say b_ij(t)](a.e Taylor series, or Bernstein series,…)

for Example with N=4, M=3 and by Taylor series we have:

now we want to approximate a function, asy f(t), in this interval with following form:

If we have:

(Tau is a constant number)
then: How can  we find L and Z matrices using maple? Is it any way? (or other softwares?)

Regards

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

evalf(10.2^20, 50);

evalf((10+1/5)^20, 50);

Where are 50 digits of the first result?

I have a matrix (1002,2) where first column isthe time and the second is numerical solution of an angle.My angle should be oscillating periodically but I am getting a noise at large times. I need to check if this noise contains certain frequencies in it so I need to plot a power spectrum of my data. How can I do that 

> restart;
> with(LinearAlgebra);
> q := a*mu^4+b*mu^3+d*mu^2+e*mu+f = 0;
> sol := solve(a*mu^4+b*mu^3+d*mu^2+e*mu+f = 0, mu);
> S[1] := allvalues(sol);
> PARAM := [a = -54/c^2-1269*A[1]/(8*c^2), b = 108/c^2+5013*A[1]/(8*c^2), d = 27-693/(2*c^2)+117*A[1]-7113*A[1]/(4*c^2), e = -27+585/(2*c^2)-111*A[1]+20439*A[1]/(16*c^2), f = 1-3*A[1]-18/c^2-8*A[1]/c^2];
> S2 := eval(S[1], PARAM);
Error, invalid input: eval received PARAM, which is not valid for its 2nd argument, eqns
> series(%, c = infinity, 3, A[1] = 0, 2]);
>
Please i mean by last statemene the solutions to be written i series as:

m1=.........+O(1/c^3)+O(A1^2)

m2=.......+O(1/c^3)+O(A1^2)

etf.

A1=0,2 means O(A1^2),therefore,i am not evaluating at .2 .

1. how to do optimization with partial differential equation as constraints in maple

2. how to do optimization with  partial differential equation as objective function in order to make output obey this model

how gr operators work?

I tried to run example given there but it is not working,

where can I get more examples to understand working of Gr operators work?

specially for raychaudhuri equations.