A Theory for the Approximation of Solutions of Boundary Value Problems on Infinite Intervals.
Abstract
An ad hoc method to solve boundary value problems which are posed on infinite intervals is to reduce the infinite interval to a finite but large one and to impose additional boundary conditions at the far end. These boundary conditions should be posed in a way so that they express the asymptotic behaviour of the actual solution well. In this paper a rigorous theory is derived which defines classes of appropriate additional boundary conditions. Appropriate is to be understood in the sense that the solutions of the approximate problems converge to the actual solution of the 'infinite' problem as the length of the finite interval tends to infinity. Moreover boundary conditions which produce convergence with the largest expectable order are devised. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1980
- Accession Number
- ADA096663
Entities
People
- Peter A. Markowich
Organizations
- University of Wisconsin–Madison