AMME2000
Yongkang XING
470019281
Section 1: Prepare Work
1)Boundary conditions: u(0,t)=0,u(9,t)=Initial condition: u(x,0)=f(x2)i)Define all the parameters:Initial conditions and boundary conditions:
0
)
0
/
s
sii)Use separation of variables:Governing Equation: 2∂t2u(x,t)=c2∂2∂ x2u(x,t)Assume a solution u(x,t)=F(x)G(t
2
∂
)
iii)Solve the resulting ODE for F(x)
:
0
)

iv)Solve the resulting ODE for G(t)
:
: