Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

I'm displaying a series of point plots as an animation, and would like to update a displayed parameter as well.  I have a nested list L[t] where there's a set of points for each t, and for each t there's also a numerical value M that I'd like to display.  (In my real problem, L[t] is the number of particles in each of several states, and M is the rms deviation from am algebraic probability distribution.)  

The closest I've gotten (for a simple L and M) is the following, but it displays all of the M values in the legend at once:

with(plots); with(Statistics);

L := [[1, 2, 3, 4, 5, 6], [2, 4, 6, 8, 10, 12]];

M := [1, 2];

display([seq(PointPlot(L[t], legend = M[t]), t = 1 .. 2)], insequence = true)

 

I don't need this to be in the legend.  Is there a way to display only the current value of M for each t?  Thanks very much.

Dear All

In following I tried to find symmetries of certain partial differential equation taken from paper "Group classification and exact solutions of generalized modified Boussinesq equation". But the determining equations are not matching with equations obtained in paper.


with(PDEtools)

DepVars := [f(u(x, t)), u(x, t)]; declare(f(u(x, t)), u(x, t))

[f(u(x, t)), u(x, t)]

 

f(u(x, t))*`will now be displayed as`*f

 

u(x, t)*`will now be displayed as`*u

(1)

PDE1 := diff(u(x, t), t, t)-delta*(diff(u(x, t), x, x, t, t))-(diff(f(u(x, t)), x, x))

diff(diff(u(x, t), t), t)-delta*(diff(diff(diff(diff(u(x, t), t), t), x), x))-((D@@2)(f))(u(x, t))*(diff(u(x, t), x))^2-(D(f))(u(x, t))*(diff(diff(u(x, t), x), x))

(2)

G := [seq(xi[j](x, t, u), j = [x, t]), seq(eta[j](x, t, u), j = [u])]

[xi[x](x, t, u), xi[t](x, t, u), eta[u](x, t, u)]

(3)

declare(G)

eta(x, t, u)*`will now be displayed as`*eta

 

xi(x, t, u)*`will now be displayed as`*xi

(4)

DetSys := DeterminingPDE(PDE1, G, integrabilityconditions = false)

{diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta, (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)), 2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)), 2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)), 4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t), 2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta, -(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), -2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta, diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta, 2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta, -(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta, -(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta, -2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta, (diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)), 2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta, diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u), diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x), diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u), diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), x), diff(diff(diff(xi[t](x, t, u), u), x), x), diff(diff(diff(xi[x](x, t, u), t), t), u), diff(diff(diff(xi[x](x, t, u), t), u), u), diff(diff(diff(xi[x](x, t, u), u), u), u), diff(diff(xi[t](x, t, u), u), u), diff(diff(xi[t](x, t, u), u), x), diff(diff(xi[t](x, t, u), x), x), diff(diff(xi[x](x, t, u), t), t), diff(diff(xi[x](x, t, u), t), u), diff(diff(xi[x](x, t, u), u), u), diff(xi[t](x, t, u), u), diff(xi[t](x, t, u), x), diff(xi[x](x, t, u), t), diff(xi[x](x, t, u), u)}

(5)

for EQ in sort([op(DetSys)], length) do EQ = 0 end do

diff(xi[t](x, t, u), u) = 0

 

diff(xi[t](x, t, u), x) = 0

 

diff(xi[x](x, t, u), t) = 0

 

diff(xi[x](x, t, u), u) = 0

 

diff(diff(xi[t](x, t, u), u), u) = 0

 

diff(diff(xi[t](x, t, u), u), x) = 0

 

diff(diff(xi[t](x, t, u), x), x) = 0

 

diff(diff(xi[x](x, t, u), t), t) = 0

 

diff(diff(xi[x](x, t, u), t), u) = 0

 

diff(diff(xi[x](x, t, u), u), u) = 0

 

diff(diff(diff(xi[t](x, t, u), u), u), u) = 0

 

diff(diff(diff(xi[t](x, t, u), u), u), x) = 0

 

diff(diff(diff(xi[t](x, t, u), u), x), x) = 0

 

diff(diff(diff(xi[x](x, t, u), t), t), u) = 0

 

diff(diff(diff(xi[x](x, t, u), t), u), u) = 0

 

diff(diff(diff(xi[x](x, t, u), u), u), u) = 0

 

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u) = 0

 

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x) = 0

 

diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u) = 0

 

diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u) = 0

 

diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta = 0

 

4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t) = 0

 

2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)) = 0

 

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)) = 0

 

2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)) = 0

 

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta = 0

 

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

 

2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)) = 0

 

-(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)) = 0

 

-(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)) = 0

 

2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta = 0

 

2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta = 0

 

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

 

-2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

 

2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

 

diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta = 0

 

-2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta = 0

 

-(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta = 0

 

-(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta = 0

 

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)) = 0

 

2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta = 0

 

(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))) = 0

(6)

DetSys1 := dsubs(diff(xi[t](x, t, u), u) = 0, diff(xi[t](x, t, u), x) = 0, diff(xi[x](x, t, u), t) = 0, diff(xi[x](x, t, u), u) = 0, diff(eta[u](x, t, u), u, u) = 0, diff(eta[u](x, t, u), x, u, t) = 0, DetSys)

{0, diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta, (diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))}

(7)

for EQ in sort([op(DetSys1)], length) do EQ = 0 end do

0 = 0

 

diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)) = 0

 

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)) = 0

 

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta = 0

 

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

 

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

 

(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)) = 0

 

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x)) = 0

(8)

The third equation in (8) can simplify last equation. This will give us eta[u][x] = 0as f[u, u] is non zero.

NULL


Download [1116]_Symmetries_Determination.mw[1116]_Group_classification_and_exact_solutions_of_generalized_modified_Boussinesq_equation.pdf

Regards

Still a little unclear what this error means tho

-f(X)/(X*(ln(X)-Psi(1-f(X))-Psi(f(X)))*GAMMA(1-m))+X*(ln(X)-Psi(1-f(X))-Psi(f(X)))/(f(X)*GAMMA(1-m)) = 0

 

Download dispatchTOshillCORE.mw

updated:

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);

 

i use 5 points trapezoid got RootOf  in result,

only 4 points is acceptable

 

when i try 5 points, there is no problem, but when more points such as

30 points, got RootOf for c sharp code

 

moreover, i got a problem when i copy the area1 result into 

visual studio c# code, it has error Integral Constant is too large

 

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4],[5, x5],[6, x6],[7, x7],[8, x8],[9, x9],[10, x10],[11, x11],[12, x12],[13, x13],[14, x14],[15, x15],[16, x16],[17, x17],[18, x18],[19, x19],[20, x20],[21, x21],[22, x22],[23, x23],[24, x24],[25, x25],[26, x26],[27, x27],[28, x28],[29, x29]], x);
f2 := solve(f=y,x);
area1 := int(f, y=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CodeGeneration):
CSharp(area1, resultname = "area1");
CSharp(area2, resultname = "area2");

i find area2 has

Warning, the function names {RootOf, Sum} are not recognized in the target language
Warning, precedence for Range unspecified
Warning, cannot translate range
area2 = RootOf((System.Double) (19276689540529530246975515949293568 * x3 - 2626509155780373903082144116707328 * x2 + 239680950855919251544490932629504 * x1 -

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

restart

with(plots):

with(LinearAlgebra):

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

(1)

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(2)

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

(3)

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(4)

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

 

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

 

phi[1]*lambda-phi[2]

 

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

(5)

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

(6)

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

(7)

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

(8)

junk(1)

I*omega*r[1]-r[2]

(9)

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

 

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

 

I*omega*r[3]-r[4]

 

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

(10)

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

(11)

``

``

``

 

Download question4.mw

pls help review this code, its doesnt return a solution

 

 

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;
for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;
NULL;
F(eta):=collect((∑)f[z](eta),eta):
Theta(eta):=collect((∑)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

 

 

 

 

 

 

im just getting a generic recursive assignment plus first unused arg error

thats what the maple engine says im doing wrong ill get the number of recursives counted but i guess it just makes me the most angry because its like the same type of error for me every ******* time

Hi all,

I was wondering how to go about validating some airfoil designs for my Formula SAE team's CFD results.  I know this is more common with simplier calculations but I'm hoping using Maple and maybe the new algebraic manipulation of non-comunitive differential operators, I could achive what I am after.   The two calculations of interest are the drag force and downforce.  Can someone shed some light? Thanks

Dear Maple users

I have done some experiments with the new Workbook feature in Maple 2016. It is a very welcome addition, indeed. Earlier I have created Maple files in which data from an external Excel file was imported and being used for certain calculations. In order to make recalculations work properly, one need to let the Excel file follow the Maple file. That's where a Workbook come in handy! I tried placing those two files in a Workbook. It didn't work completely as advertised, I think. I moved the Workbook to another location on the harddrive to make sure it wouldn't interfere with the original files outside the Workbook. Then I recalculated the Maple document inside the Workbook. The good thing: The data from the Excel file was still present. The bad thing: If I changed some data in the Excel file inside the Workbook, it didn't register in the Maple file when updating it!

Maybe I should explain that I did import data from the Excel file into Maple via the menu: Tools > Assistants > Import Data... The data was retrieved as a matrix within the Maple file and assigned to a variable and used for plots ...

Why doesn't the above procedure work properly? I hope one don't need to use the Workbook URI to reference files within the workbook. It is not that userfriendly!

 

Regards,

Erik

Hello people in mapleprimes,

I think that I found a bug.

Using the screen opened with command + f, I tried to find a v__1211 in the file I appended here.

But, when the cursor is trapped on an output part, which is a blue part, maple wouldn't continue to find the next

v__1211 anymore even if I clicked the Find Next on the screen.

If I move the cursol one line below with a hand, the Find Next butttons works again, but it is intricate.

Isn't there any good way to avoid this trouble other than not using double _, that is __.?

I hope you will give me some hint.

taro

v_1211.mw

P.S. I clicked the above link and opened that file with maple. Then, the notification telling that this is read-only file and

you cannot save this file after some modification, appeared. I don't know whether there is any problem. 

Does appending a maple file on a post on this mapleprimes always done in such a way? 

The keyboard shortcut sequence for executing an entire worksheet is Alt+e+e+w. Occasionally, I hit Alt+e+w+w by accidence. In that case, Maple sometimes, not always!?, gets completely stuck and can only be shut down through the job list window (Windows Ctrl+Alt+Del). Can anybody else replicate that? And if so, has this erratically odd behaviour been fixed in later versions of Maple?

hi....how i can extract Coefficients  (i.e. {f1[2],f2[2],f2[3],f3[2],.....f3[6]}) from every algebric equations and create matrix A ,in form AX=0, (X are f1[2],f2[2],f2[3],f3[2],.....f3[6] ) then the determinant of the matrix of coefficients (A) set to zero for obtaining unknown parameter omega.?

Note that  if m=3 then 6 equations is appeare and if m=4 then 9 equations is appeare.thus i need a procedure that works for every arbitary value of ''m''.

in attached file below m=4 thus we have 9 equations, i.e. 3 for eq1[k_] and 3 for eq2[k_] and so on...

also we should use boundary conditions for some amount of fi[j] (i=1,2,3 and j=2,3,...,7)

be extacting above Coefficients for example from first equation ,

''**:= (1/128)*f1[2]*omega^2-(1/4)*f2[2]-(1/2)*f2[3]+(1/4)*f2[4]+(1/4)*f3[2]-(1/2)*f3[3]+(1/4)*f3[4]+140*f1[2]-80*f1[3]+20*f1[4]'''

must compute

coeff(**, f1[2]); coeff(**, f2[2]) and so on...

 

 

 

 

 

fdm-maple.mw

 

 ############################Define some parameters

 

 
restart; Digits := 15; A1 := 10; A2 := 10; A3 := 10; A4 := 1; A5 := 1; A6 := 1; A7 := 1; A8 := 1; A9 := 1; A10 := 1; A11 := 1; B1 := 10; B2 := 10; B3 := 10; B4 := 1; B5 := 1; B6 := 1; B7 := 1; B8 := 1; B9 := 1; B10 := 1; B11 := 1; C1 := 10; C2 := 10; C3 := 10; C4 := 1; C5 := 1; C6 := 1; C7 := 1; C8 := 1; C9 := 1; C10 := 1; C11 := 1; C12 := 1; C13 := 1; C14 := 1; C15 := 1; C16 := 1; A12 := 1; B12 := 1; C18 := 1; C17 := 1; C19 := 1; n := 1; U := proc (x, theta) options operator, arrow; f1(x)*cos(n*theta) end proc; V := proc (x, theta) options operator, arrow; f2(x)*sin(n*theta) end proc; W := proc (x, theta) options operator, arrow; f3(x)*cos(n*theta) end proc; n := 1; m := 4; len := 1; h := len/m; nn := m+1
 ############################Define some equation

eq1[k_] := -2*f1[k]*(-A11*n^4+A10*n^2+A12*omega^2)*h^4+(A6*(f2[k-1]-f2[k+1])*n^3+A9*(f3[k-1]-f3[k+1])*n^2-A5*(f2[k-1]-f2[k+1])*n-A8*(f3[k-1]-f3[k+1]))*h^3+(4*(f1[k]-(1/2)*f1[k-1]-(1/2)*f1[k+1]))*(A3*n^2-A2)*h^2+(-A4*(f2[k-2]-2*f2[k-1]+2*f2[k+1]-f2[k+2])*n-A7*(f3[k-2]-2*f3[k-1]+2*f3[k+1]-f3[k+2]))*h+12*A1*(f1[k]+(1/6)*f1[k-2]-(2/3)*f1[k-1]-(2/3)*f1[k+1]+(1/6)*f1[k+2]):
  ``

 

 

 

 

                                     ######################################  APPLY BOUNDARY CONDITIONS

f1[nn+1] := f1[m]:
 

for k from 2 to m do eq1[k_]; eq2[k_]; eq3[k_] end do

-(1/64)*f2[4]+(1/128)*f2[3]+(1/64)*(f3[4]-(1/2)*f3[3])*(omega^2-1)-(1/64)*f1[2]+(1/32)*f1[3]+(1/64)*f1[4]-280*f3[4]-120*f3[2]+300*f3[3]+20*f3[7]

(1)

``



Download fdm-maple.mw

 

Good morning, I'm a student and I installed Maple 18 on my PC, as a "Single User Profile". Unfortunately, I had to buy another computer, so now I'm trying to install the program on my new one. Even if I enter my Purchase Code and my details, Maple says that no more activations are left in my account, even if the expiration date is on March 2020. Is it possible to activate again the program? 

Thank you,

Laura

Please help me.I don't know how to achieve the following iteration relation by maple code.iterative relationship

 

 

In a Maple Primes reply by Joel Riel on Sept. 14, 2011 he included the following command referring to warnings issued from a dsolve, numeric command having events containing a halt action:

_Env_in_maplet := true:  # incantation to suppress integrator warnings

Where can if find explanatory help for his command and any others of a similar nature?
First 152 153 154 155 156 157 158 Last Page 154 of 334