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mskalsi

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These are questions asked by mskalsi

How to apply Homotopy operator for inver...

mskalsi 290 Maple 18
euler divergence
May 25 2017
1 4

Suppose I have an expression like

Is it possible to reverse the divergence expression using homotopy operator to obtain Psi and Phi?

The above divergence expression is possible since Euler operator of the left side is zero.

Why the "pdsolve" of PDEtools package is...

mskalsi 290 Maple 18
pdsolve
May 17 2017
2 0

I am trying to solve system linear partial differential equations using command "pdsolve". I am surprised to see that the solution given by this command is not satisfying the system, instead, an additional constraint is obtained for an arbitrary function, is there something about "pdsolve" I am missing? 


 

> 

with(PDEtools):
> 

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

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

 (1)
> 

Sys := {diff(f(x, y, t, u), u, t)-(diff(f(x, y, t, u), x, y)) = 0, diff(f(x, y, t, u), u, u) = 0, diff(f(x, y, t, u), u, y) = 0, diff(f(x, y, t, u), x, u) = 0, diff(f(x, y, t, u), x, x) = 0, diff(f(x, y, t, u), y, y, y) = 0}

{diff(diff(f(x, y, t, u), t), u)-(diff(diff(f(x, y, t, u), x), y)) = 0, diff(diff(diff(f(x, y, t, u), y), y), y) = 0, diff(diff(f(x, y, t, u), u), u) = 0, diff(diff(f(x, y, t, u), u), x) = 0, diff(diff(f(x, y, t, u), u), y) = 0, diff(diff(f(x, y, t, u), x), x) = 0}

 (2)
> 

pdsolve(Sys)

{f(x, y, t, u) = (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t)}

 (3)
> 

f := proc (x, y, t, u) options operator, arrow; (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t) end proc

proc (x, y, t, u) options operator, arrow; (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t) end proc

 (4)
> 

Sys

{0 = 0, diff(_F3(t), t)-_F3(t) = 0}

 (5)
> 

``


 

Download pdsolve_command.mw

How I can find all Maxima and Minima fro...

mskalsi 290 Maple 18
maxima minima
February 22 2017
3 11

Dear All

I have a trignometric function and I plotted it in 2D. It is visible from the graph that the function has Maxima and Minima. My question is, can I located all values
 

> 

0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x)

0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x)

 (1)
> 

plot(diff(0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x), x), x = -6.2 .. 6.2)

 
> 

``


 

Download Max_Min_from_Graph.mw

of "x" corresponding to these Max. and Min. ?

How to use differetial operator two time...

mskalsi 290 Maple 18
December 08 2016
1 2

Dear All

I am trying to use differential operator two times in sucession but I am not getting desired differentiation. Please see content below:


 

> 

with(PDEtools):
> 

DepVars := [u(x, t), v(x, t), phi(x, t), psi(x, t)]; 1; declare(u(x, t), v(x, t), phi(x, t), psi(x, t))

[u(x, t), v(x, t), phi(x, t), psi(x, t)]

  

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

  

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

  

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

  

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

 (1)
> 

_local(I):
> 

I := phi(x, t)*(diff(v(x, t), x)+b*(diff(u(x, t), x, x)))+psi(x, t)*(diff(u(x, t), x, x, x)+d*(diff(v(x, t), x, x)))

phi(x, t)*(diff(v(x, t), x)+b*(diff(diff(u(x, t), x), x)))+psi(x, t)*(diff(diff(diff(u(x, t), x), x), x)+d*(diff(diff(v(x, t), x), x)))

 (2)
> 

ToJet(I, DepVars)

phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x])

 (3)
> 

T[1] := proc (f) options operator, arrow; diff(f, u[x]) end proc; 1; T[2] := proc (f) options operator, arrow; diff(f, u[x, x]) end proc; 1; T[3] := proc (f) options operator, arrow; diff(f, u[x, x, x]) end proc; 1; U[1] := proc (f) options operator, arrow; diff(f, v[x]) end proc; 1; U[2] := proc (f) options operator, arrow; diff(f, v[x, x]) end proc

proc (f) options operator, arrow; diff(f, u[x]) end proc

  

proc (f) options operator, arrow; diff(f, u[x, x]) end proc

  

proc (f) options operator, arrow; diff(f, u[x, x, x]) end proc

  

proc (f) options operator, arrow; diff(f, v[x]) end proc

  

proc (f) options operator, arrow; diff(f, v[x, x]) end proc

 (4)
> 

d := proc (f) options operator, arrow; diff(f, x)+u[x]*(diff(f, u))+u[x, x]*(diff(f, u[x]))+u[x, x, x]*(diff(f, u[x, x])) end proc

proc (f) options operator, arrow; diff(f, x)+u[x]*(diff(f, u))+u[x, x]*(diff(f, u[x]))+u[x, x, x]*(diff(f, u[x, x])) end proc

 (5)
> 

T[2](I)

0

 (6)

Why this is giving zero result ?

If I change Ito jet notation then I get result non zero result like:

> 

T[2](phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x]))

phi*b

 (7)
> 

d(T[2](phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x])))

0

 (8)

I was expecting this to be "phi[x]*b, "but instead I am getting zero result.``


 

Download operator_for_differentiation.mw

How I can use Euler-Lagrange operator fo...

mskalsi 290 Maple
November 27 2016
0 2

In paper of Nail H. Ibragimov there is operator given at equation 2.10 which he call by name Euler-Lagrange operator. How I can use this operator in Maple to derive adjoint equations ?
I have attached JPEG in which I want to apply this operator to Lagrange identity "I" for adjoint equations.

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