Case A
y
Coordinate Transformation
y
T=f(x)
Case B
T=0
y=b
T=0
T=0
T=0
x=a
x
T=0
T=0
T=f(x)
x
For the obvious reason, the solution of case A will be different from
that of case B. However, the questio
DAlemberts Solution
There is an elegant approach to solve the wave equation by
introducing new variables:
v = x + ct , z = x ct , u( x, t ) = u( v, z ) cfw_
The use of these variables is because that
FINITE DIFFERENCE
In numerical analysis, two different approaches are commonly used: In The finite difference and the finite element methods. In heat transfer problems, the finite difference method is
Fourier Transform
Fourier Integral:
f ( x ) = [ A( w) cos( wx ) + B ( w)sin( wx ) ]dw
0
1
1
where A( w) = f ( v ) cos( wv )dv, B ( w) = f ( v )sin( wv )dv
1
Therefore, f ( x ) = f ( v ) [ cos( wv
Summary of nodal finite-difference relations for various configurations
Configuration Case 1 Interior Node
Finite-Difference relations for x= y
Tm ,n +1 + Tm,n -1 + Tm +1,n + Tm -1,n - 4Tm,n = 0
Case