mehdi jafari

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9 years, 118 days

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These are questions asked by mehdi jafari

how can i get this pde solved ( numeric or analytical)
 

restart

pde__1 := diff(z(x, t), `$`(t, 2))-(diff(z(x, t), `$`(x, 2)))+z(x, t)^2 = 6*x*t*(-t^2+x^2)+x^6*t^6

diff(diff(z(x, t), t), t)-(diff(diff(z(x, t), x), x))+z(x, t)^2 = 6*x*t*(-t^2+x^2)+x^6*t^6

(1)

conds__1 := z(x, 0) = 0, z(0, t) = 0, z(1, t) = t^3

pdsolve([pde__1, conds__1])

``

NULL


 

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how can i plot this complex expression with polar plot and 3d complex plot? i want both 2d polar form and 3d plot of this.
thnx for the help

restart:with(plots,complexplot,implicitplot)

[complexplot, implicitplot]

(1)

f:=(r,theta)->I*sinh(theta-Pi/6)+cos(Pi/4)=r;

proc (r, theta) options operator, arrow; I*sinh(theta-(1/6)*Pi)+cos((1/4)*Pi) = r end proc

(2)

complexplot(f(r,theta), r = 0 .. 1, theta = 0 .. 2*Pi, coords=polar);
 

Error, (in plot) incorrect first argument [1/2*2^(1/2)-Im(sinh(theta-1/6*Pi)) = Re(r), Re(sinh(theta-1/6*Pi)) = Im(r), r = 0 .. 1]

 

 

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hi everyone
i have a nonlinear double int which want to be solved and then plot against "z" variable.
INT_problem.mw
tnx in advance

How i can i write the code for the last equation which includes summations and one product in the picture? tnx for the help.

i have two equations;i.g eq1 and eq2. i want to factor psi(x,t) in eq2 using linear differential operators and substitute it in equation 1. could anyone help?


 

restart:with(DEtools):

eq1:=E*D(II)(x)*D[1](psi)(x,t)+E*II(x)*(D[1]@@2)(psi)(x,t)-G*A(x)*psi(x,t)+G*A(x)*D[1](v)(x,t)

E*(D(II))(x)*(D[1](psi))(x, t)+E*II(x)*(D[1, 1](psi))(x, t)-G*A(x)*psi(x, t)+G*A(x)*(D[1](v))(x, t)

(1)

convert(eq1,diff)

E*(diff(II(x), x))*(diff(psi(x, t), x))+E*II(x)*(diff(diff(psi(x, t), x), x))-G*A(x)*psi(x, t)+G*A(x)*(diff(v(x, t), x))

(2)

eq2:=-(G*D[1](A)(x)*psi(x,t)+G*A(x)*D[1](psi)(x,t))+(G*D[1](A)(x)*v(x,t))+G*A(x)*(D[1]@@2)(v)(x,t)-m(x)/G*D[2](v)(x,t)

-G*(D(A))(x)*psi(x, t)-G*A(x)*(D[1](psi))(x, t)+G*(D(A))(x)*v(x, t)+G*A(x)*(D[1, 1](v))(x, t)-m(x)*(D[2](v))(x, t)/G

(3)

convert(%,diff)

-G*(diff(A(x), x))*psi(x, t)-G*A(x)*(diff(psi(x, t), x))+G*(diff(A(x), x))*v(x, t)+G*A(x)*(diff(diff(v(x, t), x), x))-m(x)*(diff(v(x, t), t))/G

(4)

isolate(convert(eq2,diff),psi)

psi = (proc (x, t) options operator, arrow; -(G^2*A(x)*(diff(psi(x, t), x))-G^2*(diff(A(x), x))*v(x, t)-G^2*A(x)*(diff(diff(v(x, t), x), x))+m(x)*(diff(v(x, t), t)))/(G^2*(diff(A(x), x))) end proc)

(5)

eval(eq1,psi(x,t)=rhs((isolate(eq2,psi))(x,t))):convert(%,diff)

E*(diff(II(x), x))*(diff(psi(x, t), x))+E*II(x)*(diff(diff(psi(x, t), x), x))+A(x)*(G^2*A(x)*(diff(_XX(x, t), x))-G^2*A(x)*(diff(diff(v(x, t), x), x))-G^2*(diff(A(x), x))*v(x, t)+m(x)*(diff(v(x, t), t)))/(G*(diff(A(x), x)))+G*A(x)*(diff(v(x, t), x))

(6)

 

 

 


 

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