Hi,

I am trying to discretize a kernel of the form $K(x,y,t,s)$. I want to evaluate a four dimensional integral of the form

\int\int\int\int K(x,y,t,s)*h_m(x)*h_n(y)*h_p(t)*h_q(s) dsdtdxdy, where limits of integration are from 0 to 1.

$h_m()$ are function of one variable.

please suggest how to evaluate this.

thanks

In the attached Maple worksheet I attempt to plot the solution of an initial value problem for a first order ODE.  DEplot fails with a cryptic message.  Strangely enough, if I give the "arrows=none" option to DEplot, it produces the correct plot!

I see this behavior in Maple 17 and 18.

Maple 11, however, works fine with or without the "arrows=none" option.

Is there an explanation for this or is it a bug?

DEplot-bug.mw

restart; macro(x = eta); einf := 4; gm1 := 10; gm2 := 5; mf := .5; pr := 6.2; le := 10; nb := .2; nt := .2; r := 2; tr := 2; bi := .5; m := 2; tr1 := 1.5;
a1 := (m+1)*(1/2);
eqs1 := diff(f(x), [`$`(x, 3)])+a1*f(x)*(diff(f(x), [`$`(x, 2)]))-m*(diff(f(x), [`$`(xx, 2)]))^2+gm1*g(x)-gm2*h(x)-mf*(diff(f(x), [`$`(x, 1)])) = 0;
eqs2 := diff(g(x), [`$`(x, 2)])+a1*pr*f(x)*(diff(g(x), [`$`(x, 1)]))+pr*nb*(diff(g(x), [`$`(x, 1)]))*(diff(h(x), [`$`(x, 1)]))+pr*nt*(diff(g(x), [`$`(x, 1)]))^2+(4/3)*r1*(diff((1+(tr-1)*g(x))^3*(diff(g(x), [`$`(x, 1)])), x)) = 0;
eqs3 := diff(h(x), [`$`(x, 2)])+a1*le*f(x)*(diff(h(x), [`$`(x, 1)]))+nt*(diff(g(x), [`$`(x, 2)]))/nb = 0;
bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(einf) = 0;
bcs2 := (D(g))(0) = bi*(g(0)-1), g(einf) = 0;
bcs3 := h(0) = 1, h(einf) = 0;
eqs := {bcs1, bcs2, bcs3, eqs1, eqs2, eqs3};
sol1 := dsolve(eqs, [f(x), g(x), h(x)], numeric, output = listprocedure);

If I typed the above line it's showing 

Error, (in dsolve/numeric/process_input) missing differential equations and initial or boundary conditions in the first argument: eqs

Kindly, I request you to do the needful as early as possible.

Hi

I am trying to implement the following basis functions $h_n(t)$. Please suggest how to implement. thanks

I have a markov matrix that is 500x500. I need to take the standard deviation of the top row of this matrix after I raise it to high powers, like 10^17 by 10^12, (from a do loop.) I would also like ot make a histogram of this data too. 

Any ideas what I can do? 

I have a pair of markov matrices that are 250x250 and 500x500 in size. I am raising these matrices to high powers, like 10^17 by 10^12. (I'm using a do loop.) If I set digits:=15, Maple will use 100% of the processor that is available. If I set digits:=16+ Maple will only use 1 thread of my processor. Why? It is the same matrix same program. The only thing that changes is the digits of accuracy. This seems exactly backwards from what it should be. As a result, my AMD9590 processor will run full blast when I choose 15 digits of accuracy and gets the biggest matrix done in 1-2 hours. If i set the accuracy to 17 digits, it takes half a day or more to do the same thing!!! 2 digits of greater accuracy should not take an additional 20 hours!

Thanks 

Hi

I need a command or code to display numerical amount of parameter (i) in below textbox

e.g. display Element 2 instead of Element i when i is equal to 2

Hello,

How can i from a randomly generated 100 numbers, output the number of unique elements...

thank you very much.

hello, 

i need to use only looping to determine the larget integer in my random list...

here is how i put it together, but my result is incorrrect... Please help.

thank you

R:=rand(1..50)

seq(R(1..50),i=1..20)

L:=[%]

max:=proc(L,maxv : : evaln)

locali;

maxv:=L[i];

for i from 1 to nops(L) do

if eval(maxv)<L[i] then maxv:=L[i]end if;
end do;

end proc;

The precise definition is that the distance between any two points of the rigid body remains constant. Although any body is deformed to move, if the deformation is small movement can be approximated by modeling it as a rigid body. Now let's see how Maple is part of the solution.

Cinematica_plana_de_cuerpos_rigidos.mw

(in spanish)

Atte.

Lenin Araujo C.

hello,

i am quite new into programming and i need help with writing a code that determines the largest integer in the list...

Please help..

Thank you 

Hello

I wantt to assigne value to a variable that doesn't exist before the radio button. How can i do that?

Could you please help me?

The issue I am currently having is that, while analyticity (and physics) indicates a certain function must have roots, fsolve is having trouble finding them. In fact, I have even found roots manually in a certain region myself, simply inputting into the function various values until I found them. However, fsolve does not seem to want to find these roots, and I believe it is a numerics issue: when I changed the digits around, for extremely low values of Digits, it would find a root (even though it was incorrect). Further, this problem arose elsewhere in the domain of interest for other values of Digits (in particular, for Digits:=5, fsolve failed in a region it had not failed before).

The region of interest is the "peak" of the output of poleR(M0, 0.935, mK), which should be somewhere around M0 = 0.95 or so. However, because fsolve cannot find the roots, the plot cannot be made.

Anyone have any ideas as to why fsolve cannot find the roots? I was also experiencing issues with some of these functions having multiple roots, which itself is weird as well (note that I am working over the complex plane).

Attached is the document.

pole-dragging-mapleprimes.mw

Any ideas?

Hi everybody!

It's nice to join in this forum.

I'm trying to get the analytic solution of the Bernouilli-Euler beam equation, with the next boundary conditions:

w(x,t) = displacements.

w(0,t) = 0   -> It's a cantilever beam. At the x=0 it's clamped.

diff(w(x,t),x) = 0.   -> the gyro in the clamp is zero.

E*I*diff(w(L,t),x,x) = 0  -> the moment at the end of the beam (x=L) is zero.

E*I*diff(w(L,t),x,x,x) = 0  -> the shear at the end of the beam (x=L) is zero too.

I'm not able to introduce the second and the third derivatives as boundary conditions in the pdsolve equation. I post the hole code:

restart;
ode := I*E*(diff(w(x, t), x, x, x, x))+m*(diff(w(x, t), t, t)) = 0;

s := pdsolve(ode, w(x, t));

ode1 := op([2, 1, 1], s);

ode2 := op([2, 1, 2], s);

f1 := op(4, rhs(ode1));

f2 := op(2, rhs(ode2));

sol1 := dsolve(ode1, f1);

sol2 := dsolve(ode2, f2);

sol := rhs(sol1)*rhs(sol2);

conds := [w(0, t) = 0, (D[1](w))(0, t) = 0, eval(I*E*(D[1, 1](w))(x, t), x = L) = 0, eval(I*E*(D[1, 1, 1](w))(x, t), x = L) = 0];

pde := [ode, conds];

pdsolve(pde, w(u, t));

And I get this error:

"Error, (in PDEtools/pdsolve) invalid input: `pdsolve/sys` expects its 1st argument, SYS, to be of type {list({`<>`, `=`, algebraic}), set({`<>`, `=`, algebraic})}, but received [I*E*(diff(diff(diff(diff(w(x, t), x), x), x), x))+m*(diff(diff(w(x, t), t), t)) = 0, [w(0, t) = 0, (D[1](w))(0, t) = 0, I*E*(D[1, 1](w))(L, t) = 0, I*E*(D[1, 1, 1](w))(L, t) = 0]]"

It's seems I'm introducing the Boundary conditions of the second and third derivatives in a wrong way, but I can't discover how to do it.

Thanks very much in advance to everybody!!

Ger89

P.D. - I have use this "tutorial" to write the code ( http://homepages.math.uic.edu/~jan/mcs494f02/Lec34/pde.html ). Thanks very much again. 

Hello

I wqant to minimize a function that has som parameters (here number of parameters are two). how can i do that?

I have attache a picture from my target function. Could you please help me?

Tahnk you.