## [Vn5socks.net] Car Update 24/7 – Good Socks 5h00 PM

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## [Vn5socks.net] Car Update 24/7 – Good Socks 10h30 PM

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Feuerhimmel
Reviewed by Feuerhimmel on
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[Vn5socks.net] Auto Update 24/7 – Good Socks 12h10 PM
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Rating: 5

## Great Britain Tier 2 Visa Lahore Pakistan. keep my passport service extra postponed

I applied for a Tier 2 UK visa on Lahore Pakistan on May 21, 2019, and decided to keep my passport service. I was told to submit my passport, which I did on June 19th. I have not received any answer from them since. Has anyone seen any similer problems here? I've contacted the UKVI hotline, but it just says it's being checked. Thanks for your help.

## Differential Equations – Using NDSolve on Wave PDE on String if the solution is given at 2 different times instead of the initial velocity?

This is a PDE from a Maple document. Mathematica DSolve can not solve it right now.

I wanted to review the Maple solution with NDSolve. This is a string of length 1, which is fixed on the left and can move freely to the right. Give a starting position and let go.

Here are the specifications of the PDE

Solve for $$0 0$$ the wave PDE
$$-u_ {tt} + u (x, t) = u_ {xx} + 2e ^ {- t} left (x – frac {1} {2} x ^ 2 + frac {1} {2} t – 1 right)$$

With boundary condition

begin {align *} u (0, t) & = 0 \ frac { partial u (1, t)} { partial x} & = 0 end {align *}

And initial conditions

begin {align *} u (x, 0) & = x ^ 2-2 x \ u (x, 1) & = u left (x, frac {1} {2} right) + e ^ {- 1} left ( frac {1} {2} x ^ 2-x right ) – left ( frac {3} {4} x ^ 2- frac {3} {2} x right) e ^ { frac {-1} {2}} end {align *}

The tricky thing is that no initial speed is given. But only starting position $$t = 0$$, and then instead a relation to the solution is given at 2 different times.

`NDSolve` Complain with this dreaded mistake

The boundary condition is not indicated on a single edge of the border
the computational domain.

And I do not know how to get rid of it. Here is the code

``````Delete everything[u, x, t];
pde = -D[u[x, t], {t, 2}]+[x, t] ==
D[u[x, t], {x, 2}]+ 2 * exp[-t]* (x - (1/2) * x ^ 2 + (1/2) * t - 1);

bc = {u[0, t] == 0, derivative[1, 0][u][1, t]    == 0};

ic = {u[x, 0] == x ^ 2 - 2 * x,
u[x, 1] == u[x, 1/2] + ((1/2) * x ^ 2 - x) * Exp[-1] - ((3 * x ^ 2) / 4 - (3/2) * x) * Exp[-2^(-1)]};

sol = NDSolve[{pde, ic, bc}, u, {x, 0, 1}, {t, 0, 1}]
``````

Here's the Maple code and the analytic solution it contains

``````pde: = -diff (u (x, t), t, t) + u (x, t) =
diff (u (x, t), x, x) + 2 * exp (-t) * (x- (1/2) * x 2 + (1/2) * t-1);
ic: = u (x, 0) = x ^ 2-2 * x,
u (x, 1) = u (x, 1/2) + (1/2) * x ^ 2-x) * exp (-1) - (3/4 * (x ^ 2) -3/2 * x) * exp (-1/2);
bc: = u (0, t) = 0, eval (diff (u (x, t), x), {x = 1}) = 0;
pdsolve ([pde, ic, bc], u (x, t))
``````

$$u (x, t) = – frac {e ^ {- t}} {2} (x ^ 2-2 x) (t-2)$$

Here is an animation of the Maple solution that I wanted to review

``````mapleSol[x_, t_] : = - (Exp[-t]/ 2) (x ^ 2 - 2 x) (t - 2)
Manipulate[
plot[mapleSol[mapleSol[mapleSol[mapleSol[x, t], {x, 0, 1}, PlotRange -> {{0, 1}, {-1, .1}}].
{{t, 0, "time"}, 0, 10, .1}
]
``````

Any suggestion how to fix the bug of NDSolve?

Using V 12 on Windows 10. ps. I also solved this by hand, but I can not find a Maple solution, and my solution looks wrong. I still have to find out why.