Is there anyway to animate d'Alemberts wave solution as time goes on? 

Suppose I have the initial value problem:

PDE:   u_tt = u_xx

ICS:    u(x,0) = x

            u_t(x,0) = f(x)

where f(x) is piecewise defined as:

f(x) = cos(pi*x), -1/2 < x < 1/2               and

             0             otherwise

Hello, I was wondering about the following.

cos(Pi/2^n) can be converted to a radical for each integer n, because cos(Pi/2)=0 is known and successively

cos(x)=sqrt( (1+cos(2x))/2 )

so in principle radical expressions should exist for all integers n. But maple only converts cos(Pi/8) to a radical, but not cos(Pi/16) and higher powers. Is there a simple way without writing an own program to obtain these radical expressions using convert(*,radical)?

Suppose two following Eqs.:

(1) du/dt+d(u*w)/dx=0

(2) dw/dt+wdw/dx=0

I want to expand u(x,t) and w(x,t) in the power series of epsilon

u=u0+epsilon*u1+epsilon^2*u2+…

w=w0+epsilon*w1+epsilon^2*w2+…

and change the variables x,t to X,T as follows

 X=(x-alpha*t) and T=beta*t,

and solving Eqs. (1) and (2) for different order of epsilon (epsilon, epsilon^2, epsilon^3,…) to finding u0,w0,u1,w1,…

How do I do that?

Thanks.

Hello

Im trying to solve an energy functional with two independant variables. so the result would be a system of PDEs.

Ive checked

DEtools-Hamilton eq

and

vector calculus-EulerLagrange(f, t, x(t))

But I couldnt figure out how to use 2 independant variables in these commands.

Your help would be much appreciated

Does there exist a way in Maple that you can detect a change in a text file without having
to constantly having to call the readdata which keep the command prompt busy in Maple.

Maple 2018  has recently has  become sluggish to start up  -and very slow to respond to input. Can anyone suggest remedies?  I have plenty of space and CPU. Other apps seem to start fine.  Can any suggest a diagnosis and/or solution?

Melvin

How do I know that what numerical method has maple used in this code.?

dsolve({eq11,eq21,eq3,eq4,bc21,bc22},numeric,continuation=lambda1,maxmesh=15000, output=array([seq( i, i=0..N,0.01 )]))

Good day.

Reading through the Fuzzy C-Means routine (attached) written by the one-and-only Carl Love, I was wondering if anybody can tell me how to specify which points in the data belong most strongly to the assigned cluster. 

In the attached routine, there are 2 cases considered; two and three clusters. 

It would be interesting to obtain a list of all points that are assigned to each respective cluster.

Thanks for reading!

Fuzzy_clusters.mw

I have question how start histogram from 0? I have vector with probablity which start from 0.

I generate samples from my probablity:

pr=values of probablity

X:=RandomVariable(ProbablityTable(pr)):

A=Sample(X,1000):

Q=Histogram(A, binwidth=1,range=0..10):

...

I try to use bindwidth=-1 but it's impossible. 

How start histogram from 0 for vectors in maple15?

Hello I am trying to compute the following expression;

(x^2r+y^2+z^2) gamma^{0} partial_{x} (-xy(1-r)) gamma^{2} partial_{y} \Psi

in which r = sqrt(1-K(x^2+y^2+z^2)), K is a constant, the gamma's are the Dirac gamma matrices and \Psi is the wave function. Essentially I would like to have partial_{x} operate on the expression to the right of it and apply product rule where there will be three terms with the last one being partia_{x} partial_{y} \Psi where it evaluates on everything expect the partial and the wavefunction, combining into the term partial_{x} partial_{y} \Psi, and if the partials are the same they combine into a single second order derivative with respect to the given variable. I have done this calculation by hand but seeing that there is an extensive amount of terms I would like to automate it using Maple. I have tried using the D() calling sequence but it doesn't quite give me what I am looking for. Is there anything documentation which will give me what I am looking for?

Hello

I have used Groebner[UnivariatePolynomial] extensively on my procedures and I wonder whether there is an improvement in speed and memory use in Maple 2020 in relation to the version I am currently using, that is, Maple 2017.  

Many thanks.

Ed

restart;
with(LinearAlgebra):
with(VariationalCalculus):
# Energie cinetique/potentiel
T := 0.5*m*(diff(r(t),t)^2+r(t)^2*diff(theta(t),t)^2)+(1/6)*m[0]*l^2*diff(theta(t),t)^2;
Ve := 0.5*k*(r(t)-r[o])^2;
Vg := -m*g*r(t)*cos(theta(t)) - 0.5*m[o]*g*l*cos(theta(t));
# Lagrangien
L := T - (Ve + Vg);
E := EulerLagrange(L,t,[theta(t),r(t)]);
EQ1:=simplify(E[1]);
EQ2:=simplify(E[2]);
dsolve({EQ1,EQ2,D(theta)(0)=0,D(r)(0)=0,theta(0)=0,r(0)=10},{r(t),theta(t)});
dsolve({EQ1,EQ2},{r(t),theta(t)});

Hello ! 

I'm currently trying to learn some advanced mechanics with the Lagrangian method. I'm ok with the physics part. I can solve small problems by hand but when I try it on maple, it won't work.

The equations I'm using have no mistakes, I'm following a book step by step. 

What I'm stuck with is to get a formula of theta and r that are only function of time (t) to then be able to plot it. And I need dsolve to work to get that.

Got a problem related to values written to a library. One of the values somehow gets lost, and I wonder if I did the definition correct.

The specific problem is, that I have defined a table with an index. The value of mytable["hello"] seems to be missing when reading the library.

TestLibrary.mw

Hello,

I am trying to solve the 6 coupled differential equation. The 6 equations have 6 functions to be solved for with 12 boundary condition. I know for a fact that the solution to this equation exists in the form of nice polynomials.

I tried to solve without constraint. The maple solves the equations for only 4 functions and other 2 have value in form of integrals.

With the equations contraints the maple gets disconnected from the kernel after 4-5 hours of evluating.

Any idea to solves this issue ?? I have attached the workbook.

Thanks.

Mota