How to use Matlab to solve this PDE?

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Ming
Ming 2013-1-12
I have a PDE problem to solve. Could anyone solve this problem with the tool in matlab? Please don't use the finite difference method. The problem is as followed:
Governing equation:
Utt=sin(a*t)*Uxx;
Boundary Conditions: U(0,t)=0; U(L,t)=0;
Initial Conditions: Ut(x,0)=0; U(x,0)=sin(6*pi*x/L);
where 'a'is a constant, you can give a positive value to it.
'U' is a form about x and t;
'Utt' means U double prime of t; 'Uxx' means U double prime of x;
'Ut'means U prime of t.

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