A Method for the Numerical Solution of Two-Point Boundary Value Problems Based on the Use of Volterra Integral.
Abstract
Suppose that a given two-point boundary value problem to be solved is a perturbation of one for which a considerable amount of analytic information is available, in particular, the Green's function of the unperturbed problem is known. In this case, one can construct an analytic method for the solution of the perturbed problem which involves only the solution of a Volterra integral equation. Discretization of this method, which is a version of the classical 'shooting' procedure, leads to a numerical technique for the solution of perturbed boundary value problems. Under suitable assumptions, convergence of the numerical method is established, and estimates are obtained for the rate of convergence. Attention is devoted to the cases in which the unperturbed differential operator is regular or mildly singular. Linear and nonlinear problems are considered. (Modified author abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1973
- Accession Number
- AD0767132
Entities
People
- H. Fujita
- Louis B. Rall
Organizations
- University of Wisconsin–Madison