
24.4. Numerical Solutions of Systems of Linear PDEs 1397
(see
help pdepe
). The class of 1D parabolic-elliptic PD Es defined in D = {a ≤ x ≤ b,
t
0
≤t ≤t
f
} to which the function
pdepe
can be applied has the form
C(x,t)u
t
= x
−m
∂
x
x
m
f(x,t,u,u
x
)
+ s(x,t,u,u
x
), (24.4.1.1)
where u is the unknown vector function that depends on the scalar space variable x and the
scalar time variable t; the flux function f and the source function s are vector functions; the
integer m ∈{0,1,2} corresponds to slab, cylindrical, and spherical symmetry, respectively;
the function C is a diagonal matrix whose diagonal entries are zero or positive (which
corresponds to elliptic or parabol ...