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 question is whether do we need to
derive the solution B from s
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 the solution of the
wave equation behaves in specific
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 used more often and will be discussed here. The finite
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 2 Node at an internal corner with convection
T, h
2(Tm-