Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

Hello, I found this very strange behavior in Maple and I can't explain why this is not working

A little bit of context first:

1. I placed a polygon as a boundary for a section and then two polygons that correspond to inner holes to the first one.
2. Then I proceed to create a regular mesh that places N x M points spread across the region (OK here)
3. A procedure checks weather or not a Point is inside the region, on the borders or in the inner holes (OK here)
4. Then I want to select the closest (but exterior) ones so I can create a path using the mesh points.
 

Here is where I find the issue. I start at a vertex called V[1,1] and I want to arrive at V[1,2] (in the document they are blue solid points marked they are near-vertices near the original polygons). The procedure that I apply finds a path towards the V[1,2] as I was expecting but when the procedure hits the V[1,2] coordinates the while loop does not stop

The condition I wrote was:    while point<>V[1,2] do  where 'point' is correctly generated by another procedure.

This happens in a 40 by 50 mesh but with other configurations it works properly (there are also another kind of errors but it's inherent to lack of optimization in my procedures).

What baffles me is why doesn't it stop the cycle, if I test the condition outside the loop it DOES recognize the points are indeed equal. Is it something in Maple or is it something in my PC?

Thanks to anyone who can see the error or the problem because I don't understand the nature of the problem.

Not_Working.mw

Problem with pdsolve/numeric


Contextualizing:

I created a routine for solving a thermo-mechanical problem. The size of the spatial domain is a function of time and the thermo-mechanical behavior of the structure.

The solution is obtained by discretizing the time domain in n intervals. The thermo-mechanical responses are obtained at each time t[i] =t[i-1]+dt.

The material exhibits elastic and elastoplastic mechanical behavior and thus the problem was divided into two consecutive phases (phase 1 and 2).

The heat problem is nonlinear because the thermal properties are variable (termal conductivity, specific heat, and density).

 

The problem:

In phase 2, the pdsolve/numeric command returns an error for the solution of the heat conduction equation (equation called pde1). I believe this error is related to the derivative of thermal conductivity k(x1) (piecewise function).

I tested many alternatives (I wrote the pde1 equation in two different ways), I checked the routine many times and I don't understand the reason for the error. With each attempt, the command returns a different error.


Thanks for your attention and help.

Problem.mw

Could anyone help me out to convert the equation into differential transform method

 

Please can you help me in resolving this error?

Here is the codeOptimal_control_model_of_DF_and_LP_2.mw

Dear maple users,

Greetings.

When converting the maple figure into EPS format (for latex) which shows white patches.

How to avoid such patches.

Dear Maple Users @acer @Carl Love @Kitonum @Preben Alsholm ,

Greetings.

How to plot a function "Am" for various values of "kt"(eg: kt=-1..1) at a point x=0.

Am vs kt.

The code has provided below.

Waiting for your response.

ktplot.mw

 

How can I generate a code to plot the optimals; h, chi and psi?

Dear all

I need to display a matrix K defined in the attached maple code.

Thanks for your help

matrix.mw

restart;
solve({l*(2*l^2*lambda^4*sigma*w*a[2]+l^2*lambda^2*mu*w*b[1]+6*l*lambda^2*m*sigma*a[0]^2-6*l*lambda^2*m*b[1]^2+6*l*m*mu^2*a[0]^2-l*lambda^2*rho*sigma*a[0]-l*mu^2*rho*a[0]+4*lambda^2*sigma*w*a[0]+4*mu^2*w*a[0]) = 0, l*(2*l^2*lambda^3*sigma*w*a[1]+6*l^2*lambda^2*mu*w*b[2]+2*l^2*lambda*mu^2*w*a[1]+12*l*lambda^2*m*sigma*a[0]*a[1]-12*l*lambda^2*m*b[1]*b[2]-l*lambda^2*rho*sigma*a[1]+12*l*m*mu^2*a[0]*a[1]-l*mu^2*rho*a[1]+4*lambda^2*sigma*w*a[1]+4*mu^2*w*a[1]) = 0, l*(5*l^2*lambda^3*sigma*w*b[2]-3*l^2*lambda^2*mu*sigma*w*a[1]-7*l^2*lambda*mu^2*w*b[2]-3*l^2*mu^3*w*a[1]+12*l*lambda^2*m*sigma*a[0]*b[2]+12*l*lambda^2*m*sigma*a[1]*b[1]-l*lambda^2*rho*sigma*b[2]+24*l*lambda*m*mu*b[1]*b[2]+12*l*m*mu^2*a[0]*b[2]+12*l*m*mu^2*a[1]*b[1]-l*mu^2*rho*b[2]+4*lambda^2*sigma*w*b[2]+4*mu^2*w*b[2]) = 0, l*(8*l^2*lambda^3*sigma*w*a[2]+6*l^2*lambda*mu^2*w*a[2]+12*l*lambda^2*m*sigma*a[0]*a[2]+6*l*lambda^2*m*sigma*a[1]^2+l^2*lambda*mu*w*b[1]-6*l*lambda^2*m*b[2]^2-l*lambda^2*rho*sigma*a[2]+12*l*m*mu^2*a[0]*a[2]+6*l*m*mu^2*a[1]^2-6*l*lambda*m*b[1]^2-l*mu^2*rho*a[2]+4*lambda^2*sigma*w*a[2]+4*mu^2*w*a[2]) = 0, -l*(4*l^2*lambda^3*mu*sigma*w*a[2]-l^2*lambda^3*sigma*w*b[1]+l^2*lambda*mu^2*w*b[1]-12*l*lambda^2*m*sigma*a[0]*b[1]+l*lambda^2*rho*sigma*b[1]-12*l*lambda*m*mu*b[1]^2-12*l*m*mu^2*a[0]*b[1]+l*mu^2*rho*b[1]-4*lambda^2*sigma*w*b[1]-4*mu^2*w*b[1]) = 0, 6*l^2*(l*lambda^2*sigma*w*a[2]+lambda^2*m*sigma*a[2]^2+l*mu^2*w*a[2]+m*mu^2*a[2]^2-lambda*m*b[2]^2) = 0, 2*l^2*(l*lambda^2*sigma*w*a[1]+6*lambda^2*m*sigma*a[1]*a[2]+3*l*lambda*mu*w*b[2]+l*mu^2*w*a[1]+6*m*mu^2*a[1]*a[2]-6*lambda*m*b[1]*b[2]) = 0, -2*l^2*(5*l*lambda^2*mu*sigma*w*a[2]-l*lambda^2*sigma*w*b[1]+5*l*mu^3*w*a[2]-6*lambda^2*m*sigma*a[1]*b[2]-6*lambda^2*m*sigma*a[2]*b[1]-l*mu^2*w*b[1]-6*lambda*m*mu*b[2]^2-6*m*mu^2*a[1]*b[2]-6*m*mu^2*a[2]*b[1]) = 0, 6*l^2*b[2]*(l*w+2*m*a[2]) = 0}, {a[0], a[1], a[2], b[1], b[2]});
Warning, solutions may have been lost
{a[0] = 0, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0}, 

   /       l rho - 4 w                                        \ 
  { a[0] = -----------, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0 }
   \          6 l m                                           / 
 

If we have an equation for the generalized Bloch sphere i.e.,

\partial_{t}(u^{2} + v^{2} + w^{2}) = 0,

where u, v and w are functions of x and t and the initial conditions u=v=0, w=-1. Then how to plot this equation on maple?

Hi all,

I have a system of nonlinear equations with for equations, 4 variables I want to solve for, and 2 parameters. All of the variables and parameters must be non-negative.

The code I used to try to do this is:

Where eqi (i = 1, ... , 4) are expression (not equations in themselves). For example, eq1 is:

 

When I try to run this code I get the following error:

"Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters"

 

Can anyone help me how I can make Maple do what I want here? :)

 

Thank you in advance,

JTamas

 Mathematical model for the temperature profiles of steel pipes quenched by water cooling rings

Hi

 Can anyone solve the given equations along with the boundary conditions analytically with Maple and draw the graphs ???????????

Dear maple users,
Greetings.
I am solving an ode problem with an analytical solution.
programming running properly, but my plot not exact with the already existing article plot. 
how to get the exact plot.

Thanking you.

Code:JVB.mw
 

restart

N := 3;

3

 

1

(1)

dsolve(diff(f(x), `$`(x, 3)));

f(x) = (1/2)*_C1*x^2+_C2*x+_C3

(2)

Rf := 2*(diff(f[m-1](x), x, x, x))-(2*mh*mh)*(diff(f[m-1](x), x))+sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1)-bet*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(f[t](x), x, x))+f[m-1-n](x)*f[n-t](x)*(diff(f[t](x), x, x, x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(f[t](x), x, x)), t = 0 .. n), n = 0 .. m-1));

2*(diff(diff(diff(f[m-1](x), x), x), x))-2*(diff(f[m-1](x), x))+sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1)-.2*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x))+f[m-1-n](x)*f[n-t](x)*(diff(diff(diff(f[t](x), x), x), x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x)), t = 0 .. n), n = 0 .. m-1))

(3)

dsolve(diff(f[m](x), x, x, x)-CHI[m]*(diff(f[m-1](x), x, x, x)) = h*H*Rf, f[m](x));

f[m](x) = Int(Int(Int(CHI[m]*(diff(diff(diff(f[m-1](x), x), x), x))+2*h*(diff(diff(diff(f[m-1](x), x), x), x))-2*h*(diff(f[m-1](x), x))+h*(sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1))-(1/5)*h*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x))+f[m-1-n](x)*f[n-t](x)*(diff(diff(diff(f[t](x), x), x), x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(diff(f[t](x), x), x)), t = 0 .. n), n = 0 .. m-1)), x), x)+_C1*x, x)+_C2*x+_C3

(4)

f[0](x) := 1-exp(x);

1-exp(x)

(5)

for m to N do CHI[m] := `if`(m > 1, 1, 0); f[m](x) := int(int(int(2*CHI[m]*(diff(f[m-1](x), x, x, x))-(2*h*H*mh*mh)*(diff(f[m-1](x), x))+h*H*(sum(f[m-1-n](x)*(diff(f[n](x), x)), n = 0 .. m-1)), x)-h*H*(sum(sum(2*f[m-1-n](x)*(diff(f[n-t](x), x))*(diff(f[t](x), x, x))+f[m-1-n](x)*f[n-t](x)*(diff(f[t](x), x, x, x))+x*(diff(f[m-1-n](x), x))*(diff(f[n-t](x), x))*(diff(f[t](x), x, x)), t = 0 .. n), n = 0 .. m-1))*bet, x)+_C1*x, x)+_C2*x+_C3; s1 := evalf(subs(x = 0, f[m](x))) = 0; s2 := evalf(subs(x = 0, diff(f[m](x), x))) = 0; s3 := evalf(subs(x = 1, f[m](x))) = 0; s := {s1, s2, s3}; f[m](x) := simplify(subs(solve(s, {_C1, _C2, _C3}), f[m](x))) end do:

f(x) := sum(f[l](x), l = 0 .. N);

1-0.7644444444e-1*exp(5.*x)*h^2*x-0.1333333333e-1*x^2*exp(5.*x)*h^2-2.675700596*exp(2.*x)*h^2*x-0.5876096022e-1*exp(6.*x)*h^3*x-0.9282030175e-2*x^2*exp(6.*x)*h^3+.9962792493*exp(3.*x)*h^3*x+.1647896790*exp(5.*x)*h^3*x+0.2066962962e-1*x^2*exp(5.*x)*h^3+3.357118680*exp(2.*x)*h^3*x-.3264340965*exp(4.*x)*h^3*x+0.3999999998e-1*exp(2.*x)*ln(exp(x))*h^2+58.61348006*h^3+1.023148148*h^2*x^3+0.1364197531e-1*ln(exp(x))*h^3*x^3-0.8954734530e-1*exp(2.*x)*h^3*x^4-.1353159884*x^3*exp(4.*x)*h^3+.7542645986*exp(3.*x)*h^3*x^2-0.2830138323e-1*x^3*h^3*exp(3.*x)-0.6455420536e-1*exp(x)*h^3*ln(exp(x))*x+0.4775858416e-1*exp(x)*h^3*ln(exp(x))*x^2+0.8888888887e-3*exp(x)*h^3*ln(exp(x))^2+8.400000000*h*exp(x)-exp(x)-0.6666666666e-1*h*ln(exp(x))+.1416666666*exp(4.*x)*h^2*x-.4790123458*exp(3.*x)*h^2*x+.1333333333*exp(3.*x)*h*x+.3791666665*exp(4.*x)*h^2-1.340020575*exp(3.*x)*h^2+.3111111109*exp(3.*x)*h+5.570191338*h^2*exp(2.*x)-.4500000000*h*exp(2.*x)-0.9874869443e-1*exp(6.*x)*h^3+.4125877323*exp(3.*x)*h^3-4.984787877*h^3*exp(2.*x)-.8010958741*exp(4.*x)*h^3+.3215641638*exp(5.*x)*h^3-5.930474628*h^2*x+36.04284024*exp(x)*h^3*x+8.324321524*x^2*h^2-.5362260993*h^3*x^3-6.207072379*exp(x)*x^2*h^3+1.664189246*exp(x)*h^3*x^3-8.237962963*h+.1200000000*exp(x)*h^2*ln(exp(x))+0.2222222222e-1*exp(3*x)*h*x+24.00299428*h^3*x-2.098561083*x^2*h^3-53.48457977*h^3*exp(x)+0.9949705035e-2*ln(exp(x))*h^3*x^4-0.7308641971e-2*ln(exp(x))*exp(4.*x)*h^3+0.8984910834e-2*ln(exp(x))*exp(3.*x)*h^3-0.3741666666e-1*ln(exp(x))*h^3*exp(2.*x)-.1188740741*exp(5.*x)*h^2-12.53662834*x^2*h+25.90916526*h^2*exp(x)-30.39962862*h^2-0.7499999999e-1*h*exp(2*x)+0.5185185185e-1*exp(3*x)*h+5.372840718*exp(x)*x^2*h^2-25.09181716*exp(x)*h^2*x+0.8976305409e-1*h^3*x^5+0.2158026099e-1*exp(7.*x)*h^3+0.8606919260e-1*h^3*x^4+0.5079365079e-3*x^3*exp(7.*x)*h^3-.3215468487*x^2*exp(4.*x)*h^3+0.1762236380e-1*exp(7.*x)*h^3*x+0.5048727639e-2*exp(7.*x)*x^2*h^3-3.116709690*exp(2.*x)*x^2*h^3+.1066289908*exp(2.*x)*h^3*x^3-8.527777777*h*x-0.2814814814e-2*ln(exp(x))*exp(4.*x)*h^3*x-0.1053497943e-2*ln(exp(x))*exp(3.*x)*h^3*x+0.4848332783e-1*h^3*x^6+.7462278773*h^2*x^4+.5519508187*exp(x)*h^3*x^4+0.9367631194e-1*exp(x)*h^3*ln(exp(x))+3.581893812*exp(2.*x)*x^2*h^2

 

 

NULL


 

Download JVB.mw

 

Analytical solution approach:

 

 

 

 

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