Boundary value application of a one-dimensional maximum principle.
Jones, James Dale
Hunt, Robert W.
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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].