
15.1. Separation of Variables (Fourier Method) 1163
TABLE 15.1
Description of auxiliary problems for Eq. (15.1.4.1) and problems for associated
functions ϕ(x) and ψ(y) that determine particular solutions of the form (15.1.4.3).
The abbreviation HB C stands for “homogeneous boundary condition”
Auxiliary
problem
Functions vanishing
in the boundary
conditions (15.1.4.14)
Eigenvalue problem
with homogeneous
boundary conditions
Another problem with one
homogeneous boundary
condition (for λ
n
found)
Problem 1
f
2
(y) = f
3
(x) = f
4
(x) = 0,
function f
1
(y) prescribed
functions ψ
n
(y) and values λ
n
to be determined
functions ϕ
n
(x)
satisfy an HBC at x = x
2
Problem 2
f
1
(y) = f
3
(x)