Assignment2.docx - AMME2000 Yongkang XING 470019281 Section...

AMME2000
Yongkang XING
470019281
Section 1: Prepare Work
1) Boundary conditions: u ( 0, t ) = 0, u ( 9, t ) =
Initial condition: u
(
x, 0
)
= f ( x
2)
i) Define all the parameters:
Initial conditions and boundary conditions:
0
)
0
/ s
s
ii) Use separation of variables:
Governing Equation:
2
∂t
2
u
(
x,t
)
= c
2
∂
2
∂ x
2
u
(
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 ) :
: