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salim-barzani

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These are questions asked by salim-barzani

How determine the complex region for 3...

salim-barzani 1560 Maple 2021
complex complexplot3d plotting
August 02 2024
1 12
> 

restart;
> 

local gamma;

gamma

 (1)
> 

with(Plot)

 

> 

params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7,theta=0,gamma=1};

{alpha = 2.5, gamma = 1, k = 3, theta = 0, w = 2, beta[3] = 3, beta[4] = 1.7}

 (2)
> 

xi := sqrt(-1/(72*alpha*beta[4]+72*gamma*beta[4]))*(2*alpha*k*t+x)

(-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)

 (3)

 

> 

sol1 := [U(xi), -k*x -(9*alpha*k^2*beta[4] + 2*beta[3]^2)/(9*beta[4])*t + theta];

[U((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)), -k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta]

 (4)

 

> 

sol2 := eval(sol1, U(xi) = -beta[3]/(3*beta[4]) + beta[3]*sinh(xi)/(6*beta[4]*cosh(xi)) + beta[3]*cosh(xi)/(6*beta[4]*sinh(xi)));

[-(1/3)*beta[3]/beta[4]+(1/6)*beta[3]*sinh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))/(beta[4]*cosh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)))+(1/6)*beta[3]*cosh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))/(beta[4]*sinh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))), -k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta]

 (5)

 

> 

solnum :=eval(sol2, params);

[-.5882352940+(.2941176471*I)*sin(.7247137946*t+0.4831425297e-1*x)/cos(.7247137946*t+0.4831425297e-1*x)-(.2941176471*I)*cos(.7247137946*t+0.4831425297e-1*x)/sin(.7247137946*t+0.4831425297e-1*x), -3*x-23.67647059*t]

 (6)
> 

plots:-complexplot3d(solnum, x = -50.. 50, t = -50..50);

Warning, unable to evaluate the function to numeric values in the region; complex values were detected

  

 
> 

NULL


if there is any other way for graph please share with me

Download complexplot3d.mw

plot solution of PDE ...

salim-barzani 1560 Maple 2021
plotting
August 01 2024
1 1 
restart;
with(Plot);
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7};
xi := beta[3]*(2*alpha*k*t + x)*sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]));
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7}

          xi := beta[3] (2 alpha k t + x) 

                                                 (1/2)
            /                 1                 \     
            |-----------------------------------|     
            \36 alpha beta[4] + 36 gamma beta[4]/     


sol1n := u(x, t) = U(xi)*exp((-sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]))*x + w*t + theta)*I);
                     /                          
                     |                          
 sol1n := u(x, t) = U|beta[3] (2 alpha k t + x) 
                     \                          

                                        (1/2)\    /  /
   /                 1                 \     |    |  |
   |-----------------------------------|     | exp|I |
   \36 alpha beta[4] + 36 gamma beta[4]/     /    \  \
                                       (1/2)                \\
  /                 1                 \                     ||
 -|-----------------------------------|      x + w t + theta||
  \36 alpha beta[4] + 36 gamma beta[4]/                     //



plot3d(rhs(sol1n), x = 0 .. 250, t = 0 .. 4);

how plot the the solution of PDE of this kind of function?

Download plot.mw

solve equations with condition parameter...

salim-barzani 1560 Maple 2021
parameters substitution differential-equations
July 30 2024
0 1

before run file remove all (:) i want calculate equation but with a condition for example: when a=4 then find other parameter in my equation with respect to a=4 find other

usesol.mw

How choose the case after finding parame...

salim-barzani 1560 Maple 2021
solve select
July 28 2024
1 5

when i finding parameter i want just choose a case for example a_1=a_1  and any other case a_2=0,and remove other case how i can do in maple

> 

restart
> 

with(PDEtools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

with(DEtools)
> 

with(DifferentialAlgebra)
> 

"with(Student[ODEs][Solve]): "
> 

with(IntegrationTools)
> 

with(inttrans)
> 

with(PDEtools)
> 

with(Physics)
> 

with(PolynomialTools)
> 

with(RootFinding)
> 

with(SolveTools)
> 

with(LinearAlgebra)
> 

with(sumtools)
> 

``
> 

ode := F(xi)^5*a[4]+F(xi)^4*a[3]+F(xi)^3*a[2]+(-k^2*a[1]+(diff(diff(F(xi), xi), xi))*a[5]-w)*F(xi)^2+(1/2)*F(xi)*(diff(diff(F(xi), xi), xi))*a[1]-(1/4)*(diff(F(xi), xi))^2*a[1] = 0
> 

NULL
> 

L := convert((cosh(xi)+sinh(xi))/(cosh(xi)-sinh(xi)), trig)
> 

"Q(xi):=L:"
> 

S := sum(A[i]*Q(xi)^i, i = 0 .. 1)+sum(B[i]*Q(xi)^(-i), i = 1 .. 1)

``

 (2)
> 

S
> 

K := F(xi) = S
> 

F1 := eval(ode, K)
> 

simplify(%)
> 

P := numer(lhs())*denom(rhs()) = numer(rhs())*denom(lhs())

Warning,  computation interrupted

  
> 

NULL
> 

solve(identity(P, xi), {k, w, A[0], A[1], B[1], a[1], a[2], a[3], a[4], a[5]})

Warning, solutions may have been lost

  

{k = k, w = w, A[0] = 0, A[1] = A[1], B[1] = 0, a[1] = a[1], a[2] = a[2], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = -4*A[0]*a[5], A[0] = A[0], A[1] = A[1], B[1] = B[1], a[1] = 0, a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = (1/2)*A[0]*(3*k^2*A[0]^2*a[4]+2*k^2*A[0]*a[3]+k^2*a[2]+4*k^2*a[5]+2*A[0]^2*a[4]+2*A[0]*a[3]+2*a[2]), A[0] = A[0], A[1] = 0, B[1] = 0, a[1] = -(1/2)*A[0]*(3*A[0]^2*a[4]+2*A[0]*a[3]+a[2]+4*a[5]), a[2] = a[2], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = w, A[0] = A[0], A[1] = 0, B[1] = 0, a[1] = a[1], a[2] = (-A[0]^3*a[4]+k^2*a[1]-A[0]^2*a[3]+w)/A[0], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = 4*A[1]*a[5]+4*B[1]*a[5], A[0] = -A[1]-B[1], A[1] = A[1], B[1] = B[1], a[1] = 0, a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = -k^2*a[1]-4*A[0]*a[5]+a[1], A[0] = A[0], A[1] = (1/4)*A[0]^2/B[1], B[1] = B[1], a[1] = a[1], a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = w, A[0] = 2*B[1], A[1] = B[1], B[1] = B[1], a[1] = a[1], a[2] = (1/2)*(k^2*a[1]+w-a[1])/B[1], a[3] = 0, a[4] = 0, a[5] = -(1/8)*(k^2*a[1]+w-a[1])/B[1]}, {k = k, w = w, A[0] = A[0], A[1] = B[1], B[1] = B[1], a[1] = 0, a[2] = w/A[0], a[3] = 0, a[4] = 0, a[5] = -(1/4)*w/A[0]}, {k = k, w = 0, A[0] = 0, A[1] = B[1], B[1] = B[1], a[1] = 0, a[2] = a[2], a[3] = 0, a[4] = 0, a[5] = -(1/4)*a[2]}

 (3)

Download choose_case.mw

simplify the multiply exponential term ...

salim-barzani 1560 Maple 2021
complex simplify assumptions
July 28 2024
1 2

i am looking for simplify this type of simplifying assume beta is Real and there is any stuf package for working with complex and conjugate automaticaly

> 

NULL
> 

restart
> 

with(inttrans)
> 

with(PDEtools)
> 

with(DEtools)
> 

with(DifferentialAlgebra)
> 

"with(Student[ODEs][Solve]): "
> 

with(IntegrationTools)
> 

with(inttrans)
> 

with(PDEtools)
> 

with(Physics)
> 

with(PolynomialTools)
> 

with(RootFinding)
> 

with(SolveTools)
> 

with(LinearAlgebra)
> 

with(sumtools)
> 

declare(u(x, t), conjugate(u(x, t)))

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

 (1)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (2)
> 

B__0 := I*G(x)^3*conjugate(G(x))^2+(2*I)*G(x)^2*(diff(G(x), x))+(2*I)*(diff(G(x), x))*G(x)*conjugate(G(x))

I*G(x)^3*conjugate(G(x))^2+(2*I)*G(x)^2*(diff(G(x), x))+(2*I)*(diff(G(x), x))*G(x)*conjugate(G(x))

 (3)
> 

"G(x):=beta*exp(I*x) "

proc (x) options operator, arrow, function_assign; Physics:-`*`(beta, exp(Physics:-`*`(I, x))) end proc

 (4)
> 

R__0 := diff(G(x), `$`(x, 2))

-beta*exp(I*x)

 (5)
> 

B__0

I*beta^3*(exp(I*x))^3*conjugate(beta*exp(I*x))^2-2*beta^3*(exp(I*x))^3-2*beta^2*(exp(I*x))^2*conjugate(beta*exp(I*x))

 (6)
> 

"#`B__0 `must equal to (I*beta^(5)*exp(I*x)) after simplify betwen expresion what code need i don't know"?""
> 

B1 := laplace(B__0, t, s)

(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)/s

 (7)
> 

R1 := laplace(R__0, t, s)

-beta*exp(I*x)/s

 (8)
> 

B2 := invlaplace(B1/s, s, t)

(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)*t

 (9)
> 

R2 := invlaplace(R1/s, s, t)

-beta*exp(I*x)*t

 (10)
> 

Sol := B2+R2

(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)*t-beta*exp(I*x)*t

 (11)
> 

simplify((-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)*t-beta*exp(I*x)*t)

(I*exp((3*I)*x)*conjugate(beta*exp(I*x))^2*beta^2-2*exp((2*I)*x)*conjugate(beta*exp(I*x))*beta-2*exp((3*I)*x)*beta^2-exp(I*x))*beta*t

 (12)
> 

expand((I*exp((3*I)*x)*conjugate(beta*exp(I*x))^2*beta^2-2*exp((2*I)*x)*conjugate(beta*exp(I*x))*beta-2*exp((3*I)*x)*beta^2-exp(I*x))*beta*t)

I*beta^3*t*(exp(I*x))^3*conjugate(beta)^2*(exp(-I*conjugate(x)))^2-2*t*beta^2*(exp(I*x))^2*conjugate(beta)*exp(-I*conjugate(x))-2*t*(exp(I*x))^3*beta^3-beta*exp(I*x)*t

 (13)
 

NULL

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