
8-56 Diff erential Equations
8.13.3 Initial and Boundary Value Problems and their
Solution
The unique solution corresponding to a particular physical problem
is obtained by use of additional information arising from the physical
situation. If this information is given on the boundary as boundary
conditions, the resulting problem is called a boundary value problem
(BVP). If this information is given at one instant as initial condi-
tions, the resulting problem is called an initial value problem (IVP).
The principle of superposition of solutions is applicable as long as
the equation is linear and homogeneous. That is, if u
n
is a solution for
each ...