find the value of $U(frac{1}{2},frac{3}{2})$ if satisfies the wave equation
$begingroup$
Given wave equation
$$
begin{aligned}
u_{tt} &= u_{xx}, 0<x<1, t>0\[1ex]
u(x,0)&=u_t(x,0)=0 ,\
u(0,t)&=sin pi t,\
u(1,t)&=t ,
end{aligned}
$$
how can we find the value
$$Uleft(frac{1}{2},frac{3}{2}right)$$
if the solution satisfies the parallelogram property
i.e. $u(A)+u(C)=u(B)+u(D)$
where $A$, $B$, $C$ and $D$ are vertices of parallelogram.
pde wave-equation
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
asked Dec 8 '18 at 16:35
learnerlearner
1158
$endgroup$
add a comment |
$begingroup$
Given wave equation
$$
begin{aligned}
u_{tt} &= u_{xx}, 0<x<1, t>0\[1ex]
u(x,0)&=u_t(x,0)=0 ,\
u(0,t)&=sin pi t,\
u(1,t)&=t ,
end{aligned}
$$
how can we find the value
$$Uleft(frac{1}{2},frac{3}{2}right)$$
if the solution satisfies the parallelogram property
i.e. $u(A)+u(C)=u(B)+u(D)$
where $A$, $B$, $C$ and $D$ are vertices of parallelogram.
pde wave-equation
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
asked Dec 8 '18 at 16:35
learnerlearner
1158
$endgroup$
$begingroup$
You have all the values on the axes, when $x = 0$ or when $t = 0$ (these are the given boundary and initial values). What have you tried that puts three vertices of a parallelogram on the axes and the fourth vertex at $(1/2, 3/2)$?
$endgroup$
– Eric Towers
Dec 8 '18 at 16:55
add a comment |
$begingroup$
Given wave equation
$$
begin{aligned}
u_{tt} &= u_{xx}, 0<x<1, t>0\[1ex]
u(x,0)&=u_t(x,0)=0 ,\
u(0,t)&=sin pi t,\
u(1,t)&=t ,
end{aligned}
$$
how can we find the value
$$Uleft(frac{1}{2},frac{3}{2}right)$$
if the solution satisfies the parallelogram property
i.e. $u(A)+u(C)=u(B)+u(D)$
where $A$, $B$, $C$ and $D$ are vertices of parallelogram.
pde wave-equation
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
asked Dec 8 '18 at 16:35
learnerlearner
1158
$endgroup$
Given wave equation
$$
begin{aligned}
u_{tt} &= u_{xx}, 0<x<1, t>0\[1ex]
u(x,0)&=u_t(x,0)=0 ,\
u(0,t)&=sin pi t,\
u(1,t)&=t ,
end{aligned}
$$
how can we find the value
$$Uleft(frac{1}{2},frac{3}{2}right)$$
if the solution satisfies the parallelogram property
i.e. $u(A)+u(C)=u(B)+u(D)$
where $A$, $B$, $C$ and $D$ are vertices of parallelogram.
pde wave-equation
pde wave-equation
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
asked Dec 8 '18 at 16:35
learnerlearner
1158
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
asked Dec 8 '18 at 16:35
learnerlearner
1158
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
edited Dec 8 '18 at 16:52
dan_fulea
6,6131312
6,6131312
asked Dec 8 '18 at 16:35
learnerlearner
1158
asked Dec 8 '18 at 16:35
learnerlearner
1158
asked Dec 8 '18 at 16:35
learnerlearner
1158
1158
$begingroup$
You have all the values on the axes, when $x = 0$ or when $t = 0$ (these are the given boundary and initial values). What have you tried that puts three vertices of a parallelogram on the axes and the fourth vertex at $(1/2, 3/2)$?
$endgroup$
– Eric Towers
Dec 8 '18 at 16:55
add a comment |
$begingroup$
You have all the values on the axes, when $x = 0$ or when $t = 0$ (these are the given boundary and initial values). What have you tried that puts three vertices of a parallelogram on the axes and the fourth vertex at $(1/2, 3/2)$?
$endgroup$
– Eric Towers
Dec 8 '18 at 16:55
$begingroup$
You have all the values on the axes, when $x = 0$ or when $t = 0$ (these are the given boundary and initial values). What have you tried that puts three vertices of a parallelogram on the axes and the fourth vertex at $(1/2, 3/2)$?
$endgroup$
– Eric Towers
Dec 8 '18 at 16:55
$begingroup$
You have all the values on the axes, when $x = 0$ or when $t = 0$ (these are the given boundary and initial values). What have you tried that puts three vertices of a parallelogram on the axes and the fourth vertex at $(1/2, 3/2)$?
$endgroup$
– Eric Towers
Dec 8 '18 at 16:55
add a comment |
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$begingroup$
You have all the values on the axes, when $x = 0$ or when $t = 0$ (these are the given boundary and initial values). What have you tried that puts three vertices of a parallelogram on the axes and the fourth vertex at $(1/2, 3/2)$?
$endgroup$
– Eric Towers
Dec 8 '18 at 16:55