On the Numerical Integration of Two-Point Boundary Value Problems for Stiff Systems of Ordinary Differential Equations.
Abstract
A class of two-point boundary value problems are considered for systems for the form dx = f(x, y, t, epsilon), edy = g sub 1 (x, t, epsilon) + g sub 2 (x, t, epsilon)y where the matrix g sub 2 (x, t, o) has a hyperbolic splitting with a fixed number of stable and unstable eigenvalues. Solutions to such boundary value problems can then be expected to have boundary layer behavior near both endpoints in the limit epsilon approaches 0 to a + value. Our analysis shows, in particular, how to determine the reduced order boundary value problem satisfied by the limiting interior solution. Orthogonal matrix methods are used to determine this reduced problem and appropriate boundary layer corrections in a computationally effective manner. Numerical experiments with model problems illustrate the possibility of multiple solutions and show how our asymptotic results can be used in combination with the COLSYS code for solving two-point problems via collocation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1980
- Accession Number
- ADA087396
Entities
People
- J. E. Flaherty
- Robert E. O'malley Jr.
Organizations
- University of Arizona