
Chapter 1 5
Separation of Variables
and Integral Transform Methods
15.1 Separation of Variables (Fourier Method)
15.1.1 Description of Separation of Variables. General Stage
of Solution
◮ Scheme of solving boundary value problems by separation of variables.
Many linear problems of mathematical physics can be solved by separation of variables.
Figure 15.1 depicts the scheme of application of this method to solve boundary value prob-
lems for second-order homogeneous linear equations of the parabolic and hyperbolic type
with homogeneous boundary conditions and nonhomogeneous initial conditions. For sim-
plicity, problems with two independent variables