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sunit

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Low level substitution of multiplication...

sunit 105 Maple
substitution
July 12 2019
2 4

Hi,

It might be a very basic question, but I am having trouble with the substitution of multiplication of symbols.  I have a equation in the format of     N*x*y-x*y+f(x,y)=0, and I need to substitute xy=1 in this equation without interferring in f(x,y).

When I am using subs commnad in maple, it is not recognizing xy nad giving me the same equation.

I really appreciate help in this matter.

Thanks in advance

Regards

Sunit

3D plot of explicit expression...

sunit 105 Maple
plot3d plotting
June 25 2018
1 0

Hi

I am having trouble in plotting the 3d plot of explicit expressions. Lets say

eq1:=f(z)

eq2:=g(z)

then how can I plot f(z) and g(z) together with z in 3d plot?

Thanks in advance

Regards

Sunit

Parallel computing in maple...

sunit 105 Maple
computation parallelization
September 15 2016
2 0

HI,

Can anyone suggest the tutorial or good examples for parallel computing in maple.

Thanks in advance.

Numerical solution of a function...

sunit 105 Maple
plot accuracy numeric
September 14 2016
0 7

Hi,

This is regarding numerical solution of a function and plot. I have a function in the form of f1(omega,arctan(f2(omega))), and i need to plot it with omega (as the expression is too long i cant insert it here). Now, if i am changing the range of omega in plot command then I am getting different plots for the small values of omega. Let's say if i change the range from 1..10 to 1..50 and look at the plot in the range of 1..3 then the plots looks different. Apart from this if i change the value of Digits  from 10 to 30 or 40 then every time i am getting an entire different  plot. As the expression if too long i cant convert it to Matlab expression and plot there. How to fix these issues. Please help me regarding this.

Regarding

Sunit

 

solving homogeneous algebraic equations ...

sunit 105 Maple
solve
September 03 2016
0 3

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)
> 

``
> 

``
> 

``

 

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