rana92

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These are replies submitted by rana92

i only use initial boundary and the error happen.
 

NULL

restart

with(plots):

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

(1)

 

vf := .8:

PDE1 := diff(u(x, t), `$`(t, 2))+2*v(t)*(diff(u(x, t), t, x))+(diff(v(t), t))*(diff(u(x, t), x))+(v(t)^2-1)*(diff(u(x, t), `$`(x, 2)))+vf^2*(diff(u(x, t), `$`(x, 4)))+gam*(diff(u(x, t), `$`(x, 4), t)+v(t)*(diff(u(x, t), `$`(x, 5))))-v2*(diff(u(x, t), `$`(x, 2), `$`(t, 2))+(diff(v(t), t))*(diff(u(x, t), `$`(x, 3)))+2*v(t)*(diff(u(x, t), `$`(x, 3), t))+v(t)^2*(diff(u(x, t), `$`(x, 4))))-tau^2*(diff(u(x, t), `$`(x, 2), `$`(t, 2))+2*v(t)*(diff(u(x, t), `$`(x, 3), t))+(diff(v(t), t))*(diff(u(x, t), `$`(x, 3)))+(v(t)^2-1)*(diff(u(x, t), `$`(x, 4)))-v2*(diff(u(x, t), `$`(x, 4), `$`(t, 2))+(diff(v(t), t))*(diff(u(x, t), `$`(x, 5)))+2*v(t)*(diff(u(x, t), `$`(x, 5), t))+v(t)^2*(diff(u(x, t), `$`(x, 6)))))-1.5*v1^2*(diff(u(x, t), `$`(x, 2)))*(diff(u(x, t), x))^2-`ζb`*((diff(u(x, t), t, `$`(x, 2)))*(diff(u(x, t), x))^2+2*v(t)*(diff(u(x, t), `$`(x, 2)))^2*(diff(u(x, t), x))+2*(diff(u(x, t), t, x))*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 2)))+v(t)*(diff(u(x, t), `$`(x, 3)))*(diff(u(x, t), x))^2)+tau^2*v1^2*(1.5*(diff(u(x, t), `$`(x, 4)))*(diff(u(x, t), x))^2+9*(diff(u(x, t), `$`(x, 3)))*(diff(u(x, t), `$`(x, 2)))*(diff(u(x, t), x))+3*(diff(u(x, t), `$`(x, 2)))^3)+tau^2*`ζb`*((diff(u(x, t), `$`(x, 4), t))*(diff(u(x, t), x))^2+6*(diff(u(x, t), `$`(x, 3), t))*(diff(u(x, t), `$`(x, 2)))*(diff(u(x, t), x))+6*(diff(u(x, t), `$`(x, 2), t))*(diff(u(x, t), `$`(x, 2)))^2+6*(diff(u(x, t), `$`(x, 2), t))*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 3)))+6*(diff(u(x, t), x, t))*(diff(u(x, t), `$`(x, 2)))*(diff(u(x, t), `$`(x, 3)))+2*(diff(u(x, t), x, t))*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 4)))+v(t)*(diff(u(x, t), x))^2*(diff(u(x, t), `$`(x, 5)))+6*v(t)*(diff(u(x, t), `$`(x, 3)))^2*(diff(u(x, t), x))+12*v(t)*(diff(u(x, t), `$`(x, 2)))^2*(diff(u(x, t), `$`(x, 3)))+8*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 2)))*(diff(u(x, t), `$`(x, 4)))) = 0

diff(diff(u(x, t), t), t)+2*(diff(diff(u(x, t), t), x))+.639*(diff(diff(diff(diff(u(x, t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))-0.1e-2*(diff(diff(diff(diff(u(x, t), t), t), x), x))-0.2e-2*(diff(diff(diff(diff(u(x, t), t), x), x), x))-1350.0*(diff(diff(u(x, t), x), x))*(diff(u(x, t), x))^2-20*(diff(diff(diff(u(x, t), t), x), x))*(diff(u(x, t), x))^2-40*(diff(diff(u(x, t), x), x))^2*(diff(u(x, t), x))-40*(diff(diff(u(x, t), t), x))*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))-20*(diff(diff(diff(u(x, t), x), x), x))*(diff(u(x, t), x))^2 = 0

(2)

PDE2 := diff(y(x, t), `$`(t, 2))+2*v(t)*(diff(y(x, t), t, x))+(diff(v(t), t))*(diff(y(x, t), x))+(v(t)^2-1)*(diff(y(x, t), `$`(x, 2)))+vf^2*(diff(y(x, t), `$`(x, 4)))+gam*(diff(y(x, t), `$`(x, 4), t)+v(t)*(diff(y(x, t), `$`(x, 5))))-v2*(diff(y(x, t), `$`(x, 2), `$`(t, 2))+(diff(v(t), t))*(diff(y(x, t), `$`(x, 3)))+2*v(t)*(diff(y(x, t), `$`(x, 3), t))+v(t)^2*(diff(y(x, t), `$`(x, 4))))-tau^2*(diff(y(x, t), `$`(x, 2), `$`(t, 2))+2*v(t)*(diff(y(x, t), `$`(x, 3), t))+(diff(v(t), t))*(diff(y(x, t), `$`(x, 3)))+(v(t)^2-1)*(diff(y(x, t), `$`(x, 4)))-v2*(diff(y(x, t), `$`(x, 4), `$`(t, 2))+(diff(v(t), t))*(diff(y(x, t), `$`(x, 5)))+2*v(t)*(diff(y(x, t), `$`(x, 5), t))+v(t)^2*(diff(y(x, t), `$`(x, 6)))))-1.5*v1^2*(diff(y(x, t), `$`(x, 2)))*(diff(y(x, t), x))^2-`ζb`*((diff(y(x, t), t, `$`(x, 2)))*(diff(y(x, t), x))^2+2*v(t)*(diff(y(x, t), `$`(x, 2)))^2*(diff(y(x, t), x))+2*(diff(y(x, t), t, x))*(diff(y(x, t), x))*(diff(y(x, t), `$`(x, 2)))+v(t)*(diff(y(x, t), `$`(x, 3)))*(diff(y(x, t), x))^2)+tau^2*v1^2*(1.5*(diff(y(x, t), `$`(x, 4)))*(diff(y(x, t), x))^2+9*(diff(y(x, t), `$`(x, 3)))*(diff(y(x, t), `$`(x, 2)))*(diff(y(x, t), x))+3*(diff(y(x, t), `$`(x, 2)))^3)+tau^2*`ζb`*((diff(y(x, t), `$`(x, 4), t))*(diff(y(x, t), x))^2+6*(diff(y(x, t), `$`(x, 3), t))*(diff(y(x, t), `$`(x, 2)))*(diff(y(x, t), x))+6*(diff(y(x, t), `$`(x, 2), t))*(diff(y(x, t), `$`(x, 2)))^2+6*(diff(y(x, t), `$`(x, 2), t))*(diff(y(x, t), x))*(diff(y(x, t), `$`(x, 3)))+6*(diff(y(x, t), x, t))*(diff(y(x, t), `$`(x, 2)))*(diff(y(x, t), `$`(x, 3)))+2*(diff(y(x, t), x, t))*(diff(y(x, t), x))*(diff(y(x, t), `$`(x, 4)))+v(t)*(diff(y(x, t), x))^2*(diff(y(x, t), `$`(x, 5)))+6*v(t)*(diff(y(x, t), `$`(x, 3)))^2*(diff(y(x, t), x))+12*v(t)*(diff(y(x, t), `$`(x, 2)))^2*(diff(y(x, t), `$`(x, 3)))+8*(diff(y(x, t), x))*(diff(y(x, t), `$`(x, 2)))*(diff(y(x, t), `$`(x, 4)))) = 0

diff(diff(y(x, t), t), t)+2*(diff(diff(y(x, t), t), x))+.639*(diff(diff(diff(diff(y(x, t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(y(x, t), t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(y(x, t), x), x), x), x), x))-0.1e-2*(diff(diff(diff(diff(y(x, t), t), t), x), x))-0.2e-2*(diff(diff(diff(diff(y(x, t), t), x), x), x))-1350.0*(diff(diff(y(x, t), x), x))*(diff(y(x, t), x))^2-20*(diff(diff(diff(y(x, t), t), x), x))*(diff(y(x, t), x))^2-40*(diff(diff(y(x, t), x), x))^2*(diff(y(x, t), x))-40*(diff(diff(y(x, t), t), x))*(diff(y(x, t), x))*(diff(diff(y(x, t), x), x))-20*(diff(diff(diff(y(x, t), x), x), x))*(diff(y(x, t), x))^2 = 0

(3)

f := proc (x) options operator, arrow; 0.1e-1*sin(Pi*x/L) end proc:

u(x, 0) = 0.1e-1*sin(Pi*x)

 

y(x, 0) = 0.1e-1*sin(Pi*x)

 

{diff(diff(u(x, t), t), t)+2*(diff(diff(u(x, t), t), x))+.639*(diff(diff(diff(diff(u(x, t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))-0.1e-2*(diff(diff(diff(diff(u(x, t), t), t), x), x))-0.2e-2*(diff(diff(diff(diff(u(x, t), t), x), x), x))-1350.0*(diff(diff(u(x, t), x), x))*(diff(u(x, t), x))^2-20*(diff(diff(diff(u(x, t), t), x), x))*(diff(u(x, t), x))^2-40*(diff(diff(u(x, t), x), x))^2*(diff(u(x, t), x))-40*(diff(diff(u(x, t), t), x))*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))-20*(diff(diff(diff(u(x, t), x), x), x))*(diff(u(x, t), x))^2 = 0, diff(diff(y(x, t), t), t)+2*(diff(diff(y(x, t), t), x))+.639*(diff(diff(diff(diff(y(x, t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(y(x, t), t), x), x), x), x))+0.5e-2*(diff(diff(diff(diff(diff(y(x, t), x), x), x), x), x))-0.1e-2*(diff(diff(diff(diff(y(x, t), t), t), x), x))-0.2e-2*(diff(diff(diff(diff(y(x, t), t), x), x), x))-1350.0*(diff(diff(y(x, t), x), x))*(diff(y(x, t), x))^2-20*(diff(diff(diff(y(x, t), t), x), x))*(diff(y(x, t), x))^2-40*(diff(diff(y(x, t), x), x))^2*(diff(y(x, t), x))-40*(diff(diff(y(x, t), t), x))*(diff(y(x, t), x))*(diff(diff(y(x, t), x), x))-20*(diff(diff(diff(y(x, t), x), x), x))*(diff(y(x, t), x))^2 = 0}

(4)

``

sols := pdsolve(sys1)

[[diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x) = 8000.*(diff(diff(u(x, t), t), x))*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))+8000.*(diff(diff(u(x, t), x), x))^2*(diff(u(x, t), x))+270000.*(diff(diff(u(x, t), x), x))*(diff(u(x, t), x))^2+4000.*(diff(diff(diff(u(x, t), t), x), x))*(diff(u(x, t), x))^2+4000.*(diff(diff(diff(u(x, t), x), x), x))*(diff(u(x, t), x))^2-200.*(diff(diff(u(x, t), t), t))-400.*(diff(diff(u(x, t), t), x))-127.8000000*(diff(diff(diff(diff(u(x, t), x), x), x), x))-1.*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))+.2000000000*(diff(diff(diff(diff(u(x, t), t), t), x), x))+.4000000000*(diff(diff(diff(diff(u(x, t), t), x), x), x))], [diff(diff(diff(diff(diff(y(x, t), x), x), x), x), x) = 8000.*(diff(diff(y(x, t), t), x))*(diff(y(x, t), x))*(diff(diff(y(x, t), x), x))+8000.*(diff(diff(y(x, t), x), x))^2*(diff(y(x, t), x))+270000.*(diff(diff(y(x, t), x), x))*(diff(y(x, t), x))^2+4000.*(diff(diff(diff(y(x, t), t), x), x))*(diff(y(x, t), x))^2+4000.*(diff(diff(diff(y(x, t), x), x), x))*(diff(y(x, t), x))^2-200.*(diff(diff(y(x, t), t), t))-400.*(diff(diff(y(x, t), t), x))-127.8000000*(diff(diff(diff(diff(y(x, t), x), x), x), x))-1.*(diff(diff(diff(diff(diff(y(x, t), t), x), x), x), x))+.2000000000*(diff(diff(diff(diff(y(x, t), t), t), x), x))+.4000000000*(diff(diff(diff(diff(y(x, t), t), x), x), x))]]

(5)

sol1 := sols[1]; sol2 := sols[2]; sys11 := simplify(subs(IC1, subs(t = 0, sol1))); sys12 := simplify(subs(IC2, subs(t = 0, sol2)))

[diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x) = 8000.*(diff(diff(u(x, t), t), x))*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))+8000.*(diff(diff(u(x, t), x), x))^2*(diff(u(x, t), x))+270000.*(diff(diff(u(x, t), x), x))*(diff(u(x, t), x))^2+4000.*(diff(diff(diff(u(x, t), t), x), x))*(diff(u(x, t), x))^2+4000.*(diff(diff(diff(u(x, t), x), x), x))*(diff(u(x, t), x))^2-200.*(diff(diff(u(x, t), t), t))-400.*(diff(diff(u(x, t), t), x))-127.8000000*(diff(diff(diff(diff(u(x, t), x), x), x), x))-1.*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))+.2000000000*(diff(diff(diff(diff(u(x, t), t), t), x), x))+.4000000000*(diff(diff(diff(diff(u(x, t), t), x), x), x))]

 

[diff(diff(diff(diff(diff(y(x, t), x), x), x), x), x) = 8000.*(diff(diff(y(x, t), t), x))*(diff(y(x, t), x))*(diff(diff(y(x, t), x), x))+8000.*(diff(diff(y(x, t), x), x))^2*(diff(y(x, t), x))+270000.*(diff(diff(y(x, t), x), x))*(diff(y(x, t), x))^2+4000.*(diff(diff(diff(y(x, t), t), x), x))*(diff(y(x, t), x))^2+4000.*(diff(diff(diff(y(x, t), x), x), x))*(diff(y(x, t), x))^2-200.*(diff(diff(y(x, t), t), t))-400.*(diff(diff(y(x, t), t), x))-127.8000000*(diff(diff(diff(diff(y(x, t), x), x), x), x))-1.*(diff(diff(diff(diff(diff(y(x, t), t), x), x), x), x))+.2000000000*(diff(diff(diff(diff(y(x, t), t), t), x), x))+.4000000000*(diff(diff(diff(diff(y(x, t), t), x), x), x))]

 

Error, (in simplify/float) invalid input: diff received 0, which is not valid for its 2nd argument

 

Error, (in simplify/float) invalid input: diff received 0, which is not valid for its 2nd argument

 

``

 

 

NULL

NULL


 

Download pdeosl.mw

@tomleslie 

@tomleslie 

i tried the pdsolve, but it doesnot work. i just want to know that is another way in maple to do or not.

thank alot for your attention.

i cant understand.

may you help me?could you share a code for such problem?

thank you for your reply

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