## Optimization of multivariate functions with inequa...

Asked by:

I need to maximize two multivariate objective functions (f(x1,y1,z1,t1) and g(x2,y2,z2,t2)) with inequality and nonnegativity constraints (x1, x2>0 and y1, z1, t1, y2, z2, t2 >=0). I am looking for parametric not numerical solutions.

What is the best way to find the solution to such a problem using maple?

## Plot a equation......

Asked by:

Hi:

i will plot the following equation so that the horizontal axis in terms of omega and vertical axis in terms of a,but i can not do it,can i help me?

equation:

## How to resolve an equation with pdsolve? KDV equat...

Asked by:

Hi ,

I would like to resolve the Kortweg and de Devries equation :

> KDV2:= diff( u(X,T), T)+ 6*u(X,T)*diff(u(X,T),X)+ diff(u(X,T),X\$3);

I used pdsolve but I have a problem to enter the IBC :

I want

u(infinity, t) =0
u( -infinity, t )=0

u ( x, 0 ) = 1

So I did :

> SOL:=pdsolve(diff( u(X,T), T)+ 6*u(X,T)*diff(u(X,T),X)+ diff(u(X,T),X\$3)=0,{u(-10, T) = 0, u(10, T) = 0, u(X, 0) =1},numeric,time=T,range=-10..10);

But it doesn't work.

( I remplace infinity by 10 because then I want the graphic representation of the solution )

Could you help me please ?

## Pi Symbol not diplayed...

Asked by:

Hi,

I am completely new to Maple (and this kind of software in general).

I am just on my first steps of learning...but I quickly noticed, that if I write Pi and hit enter, I do not get

the well-known greek Pi-symbol. I get an ordinary "p" as the result.

I checked the greek-palette...nearly all items in this palette are ordinary letters.

Does anyone have an idea whats wrong?

BTW: I don`t know if it could have to do with that, but I use a german windows 7 installation.

Thank you,

regards,

Kai

## How to create linearized model for a single degree...

Asked by:

Hi

I want to create a linearied model for a single or multi degree of freedom vibration system by MapleSim. i faced a lot of problem such as causalize ports, i search the user manual but i didn't find it useful. i attach a very simply one degree of freedom vibration system. i wondering if every one create a linearized model for it. my final goal is governing the equation and determine the natural frequency with nyquist plots. i have mapleSim 6.2 and Maple 17. Thanks

prob1.msim

## How to solve for m?...

Asked by:

Hello,

restart:

F+(1/4)*(4*(-Lambda)^(3/2)*h*m^2-2*sqrt(-Lambda)*exp(Lambda*h^2*m^2)*h*m+sqrt(Pi)*erf(h*m*sqrt(-Lambda)))/(m^2*(-Lambda)^(3/2)) = 0;

how to solve this for m for real roots, where the rest are constants with Lambda>0.

## Equation for a curve......

Asked by:

Hi:

I have a curve(plot) in Maple and i should find the math equation for it,everybody can help me how to find it?

## Solution of system of nonlinear ODEs...

Asked by:

AOA... I want to solve the following system in maple pl help

sys_ode := diff(y(eta), eta, eta, eta)+3*y(eta)*(diff(y(eta), eta, eta))-2*(diff(y(eta), eta))^2+x(eta) = 0, diff(x(eta), eta, eta)+3*Pr*y(eta)*(diff(x(eta), eta)) = 0

ics := y(0) = 0, (D(y))(0) = 0, (D(y))(infinity) = 0, x(0) = 1, x(infinity) = 0

Help.mw

## Plot numerical solution ...

Asked by:

Dear all;

Please give me few minutes to correct the output of this procedure.Many thinks.
We will solve the waves equations: diff(f(x,y,t),t\$2)=c^2*( diff(f(x,y,t),x\$2) +diff(f(x,y,t),y\$2));  where (x,y,t) in [0,1]*[0,1]*[0,T] using finite difference.  With Initial boundary conditions: [u(0,y,t)=u(1,y,t)=0],   [u(x,0,t)=u(x,1,t)=0],  [u(x,y,0)=f(x,y),   diff(u(x,y,0),t)=g(x,y)]... The code is done and perfect but....The output of this procedure is Nothing. How can I plot the solution...

f:=(x,y)->x*(x-1)*y*(y-1);
g:=(x,y)->0;
analytical_sol:=proc(dx,dy,dt,Tf)
local Ft, Fx,Fy,x,y, c1,c2,c,j,k,i,u;
Ft := floor(Tf/dt)+1;
Fx := floor(1/dx)+1;
Fy := floor(1/dy)+1;
x:=[seq(0..1,dx)]:
y:=[seq(0..1,dy)]:
c1 := (c*dt/dx)^2;
c2 := (c*dt/dy)^2;
#Initial position
for j from  1 to Fx do
for k from 1 to Fy do
u[j,k,1] := f(-dx + j*dx, -dy + k*dy) -dt*g(-dx+j*dx, -dy + k*dy);
u[j,k,2] := f(-dx + j*dx, -dy +k*dy);
end do;
end do;

# Boundary values j=1
for i from  1 to Ft +1 do
for k from 1 to Fy do
u[1,k,i] := 0;
end do;
for k from 1 to Fy do
u[Fx,k,i] := 0;
end do;

for j from 1 to Fx do
u[j,1,i] := 0;
end do;

for j from 1 to Fx do
u[j,Fy,i] := 0;
end do;
end do;

for i from 3 to Ft + 1 do
for j from 2 to Fx-1 do
for k from 2 to Fy-1 do
u[j, k, i] := 2*u[j,k,i-1] - u[j,k,i-2] + c1*(u[j+1,k,i-1]-2*u[j,k,i-1]+u[j-1,k,i-1]) + c2*(u[j,k+1,i-1] - 2*u[j, k, i-1] + u[j,k-1, i-1]);
end do;
end do;
end do;
return Matrix([seq([seq([seq(u[i,j,k],i=1..Fx)],j=1..Fy)],k=1..Ft)]):
end proc:

## Try the test
f:=(x, y) -> x (x - 1) y (y - 1)
g:=(x, y) -> 0;
analytical_sol(0.1,0.1,0.1,2);

## Solve equation in maple...

Asked by:

Hi:

i have a problem,every body can help me?

my equations:

## How do I duplicate complex arrays?...

Asked by:

Hello,

As a means of encoding information, I'm working with nested array objects (I had originally used lists, but they became too large and Maple suggested that I use arrays). The nesting should be at most four deep, but the nested arrays can have varying lengths. In order to work with the arrays, I have a series of procedures that manipulate a given array and update the existing array object to contain the result. The issue that I have is that one of my procedures needs to simultaneously use both the original array and a modified version of the array, but once the modification is performed, the original version no longer exists.

Ultimately, my issue boils down to this: is there a clean (or messy, I'm not picky) way to duplicate an array so that there are two copies of the array in memory? Just writting Array2 := Array1 just creates another pointer to the same array in memory from what I can tell, so that doesn't work. There is a function copy, but it doesn't seem to work on nested arrays.

For example, running the following does not modify Array2.

Array1 := Array([Array([1, 2]), Array([3, 4])]);
Array2 := Array([Array([1, 2]), Array([5, 6])]);
copy(Array1, Array2);

Indeed, neither does

Array1 := Array([Array([1, 2]), Array([3, 4])]);
Array2 := Array([Array([1, 2]), Array([5, 6])]);
copy(Array1(2), Array2(2));

Unfortunately, the latter case would seem to mean that I can't just write a procedure to recurse through my layers of arrays and copy piecewise either.

Thanks in advance for any help.

## How to simplify a simple unequeation...

Asked by:

Can anybody tell me what I'm doing wrong?
Or does anybody have some tips for things like this? (Things like this occur often)

Stephan

## Solve a an array...

Asked by:

Hello,

Anyone can help me with the problem ?

I want to solve b1..b50

> restart; with(plots); with(LinearAlgebra); with(Statistics);
> m0 := proc (t) options operator, arrow; 1-exp((-1)*t*.5) end proc;
t -> 1 - exp((-1) t 0.5)
> m := proc (t) options operator, arrow; (1/(1+exp(-t+5))-0.67e-2)*1.0067 end proc;
/ 1 \
t -> |--------------- - 0.0067| 1.0067
\1 + exp(-t + 5) /
> n[max] := 10; delt := .2; n := n[max]/delt;
10
0.2
50.00000000
> T := Vector(50);
> b := vector(50); evalm(b);

> for i from 2 to n do T[i] := T[i-1]+delt end do;
> fun := proc (t) options operator, arrow; add(b[i]*m0(t-T[i]), i = 1 .. n) end proc;
> fun(t);
> fu := vector(50);

> for x to 49 do fu[x] := fun(x*delt) = m(x*delt) end do;
> s := solve({fu[1 .. 50]}, {b[1 .. 50]});

Thanks,

gerst

## Can one prohibit the automatic loading of files?...

Asked by:

Hello,

sometimes I observe extreme delays when simply entering a variable name like fooBar; right after starting a Maple session. This happens when the current directory contains a file with that name, because Maple automatically loads this file.

For example, if I create an empty file fooBar.m and start a Maple session,

`> fooBar;Error, `./fooBar.m` is an incorrect or outdated .m file`

raises an error. More often however, I have some huge Maple files in the working directory and whenever I use (by chance) a variable name in the Maple session that matches a filename, Maple tries to load the corresponding file.

Is there a documentation of this behaviour and a possibility to stop this automatic loading of files?

Thanks,

Erik

## HFloat Error solving partial differential equation...

Asked by:

When trying to solve a set of partial differential equations, I always get the following error. I don't know what it means. Can somebody help me?

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