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Question: Why simplify deteriorate my integral equations?

Question:Why simplify deteriorate my integral equations?

mehdibgh 240 Maple
simplify
June 08 2017
1

I did change of variables as below:

 


 

``

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restart

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

  
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``
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UP := Int(1/2*(K__ux0*u0(x, y, t)^2+K__vx0*v0(x, y, t)^2+K__wx0*w0(x, y, t)^2+`K__φx0`*phi(x, y, t)^2+`K__ψx0`*psi(x, y, t)^2), y = 0 .. b)+Int(1/2*(K__uxa*u0(x, y, t)^2+K__vxa*v0(x, y, t)^2+K__wxa*w0(x, y, t)^2+`K__φxa`*phi(x, y, t)^2+`K__ψxa`*psi(x, y, t)^2), y = 0 .. b)+Int(1/2*(K__uy0*u0(x, y, t)^2+K__vyb*v0(x, y, t)^2+K__wyb*w0(x, y, t)^2+`K__φyb`*phi(x, y, t)^2+`K__ψy0`*psi(x, y, t)^2), x = 0 .. a)+Int(1/2*(K__uyb*u0(x, y, t)^2+K__vyb*v0(x, y, t)^2+K__wyb*w0(x, y, t)^2+`K__φyb`*phi(x, y, t)^2+`K__ψyb`*psi(x, y, t)^2), x = 0 .. a):
> 

varchange := {t = a*tau*sqrt(rho/A__ref), x = (1/2)*a*(Zeta+1), y = (1/2)*b*(eta+1), phi(x, y, t) = h*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau), psi(x, y, t) = h*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau), u0(x, y, t) = h*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau), v0(x, y, t) = h*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau), w0(x, y, t) = h*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)}:
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``
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Ut := PDEtools:-dchange(varchange, UP, [`#mover(mi("u"),mo("&uminus0;"))`, `#mover(mi("v"),mo("&uminus0;"))`, `#mover(mi("w"),mo("&uminus0;"))`, `#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`, `#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`, Zeta, eta, tau], params = [a, b, rho, A__ref]):
> 

Ut

Int((1/2)*((1/2)*K__ux0*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vx0*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wx0*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φx0`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψx0`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*b, eta = -1 .. 1)+Int((1/2)*((1/2)*K__uxa*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vxa*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wxa*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φxa`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψxa`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*b, eta = -1 .. 1)+Int((1/2)*((1/2)*K__uy0*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vyb*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wyb*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φyb`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψy0`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*a, Zeta = -1 .. 1)+Int((1/2)*((1/2)*K__uyb*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vyb*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wyb*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φyb`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψyb`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*a, Zeta = -1 .. 1)

 (1)
> 

simplify(Ut)

(1/4)*(b*(Int(K__ux0*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__vx0*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__wx0*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__φx0`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__ψx0`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2, _a = -1 .. 1))+b*(Int(K__uxa*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__vxa*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__wxa*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__φxa`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__ψxa`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2, _a = -1 .. 1))+a*(Int(K__uy0*`#mover(mi("u"),mo("&uminus0;"))`(_a, eta, tau)^2+K__vyb*`#mover(mi("v"),mo("&uminus0;"))`(_a, eta, tau)^2+K__wyb*`#mover(mi("w"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__φyb`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__ψy0`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2, _a = -1 .. 1)+Int(K__uyb*`#mover(mi("u"),mo("&uminus0;"))`(_a, eta, tau)^2+K__vyb*`#mover(mi("v"),mo("&uminus0;"))`(_a, eta, tau)^2+K__wyb*`#mover(mi("w"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__φyb`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__ψyb`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2, _a = -1 .. 1)))*h^2

 (2)
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``
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``


 

Download simplifyss.mw

 

But I amezed when I use simplify command deteriorate my eq.

 

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