Boundary value application of a one-dimensional maximum principle.
boundaryvalueapp00jone.pdf (3.269Mb)Abstract
The problem considered is the application of a one -dimensional
maximum principle to second order, linear differential equations of
the form
u'' + g(x)u' + h(x)u = f(x) for a < x < b
with associated general boundary conditions to obtain functions z₁(x) and z₂(x) such that
z₂(x) ≤ u(x) ≤ z₁(x)
on [a,b]. The functions f,g and h are assumed to be bounded. We wish
to determine the behavior of the solution u(x) on [a,b] and also to
obtain reliable numerical estimates of u.
The basic concepts in the theoretical background are expanded
versions of a presentation in Protter and Weinberger [Ref. 4].