Publication Date

10-21-1970

Abstract

I. The existence of eigenvalues is shown for certain classes of integral equations with continuous kernels. A number of interesting and useful results are thereby treated in a unified and relatively elementary way. The simplicity of these new proofs make the results accessible to introductory courses on the theory of integral equations.

II. Collocation with piecewise polynomial functions is developed as a method for solving two-point bour:rlary value problems. Convergence is shown for a general class of linear problems and a rather broad class of nonlinear problems. Some computational examples are presented to illustrate the wide applicability and efficiency of the procedure.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Lawrence F. Shampine

Second Committee Member

Unknown

Third Committee Member

Bernard Epstein

Document Type

Dissertation

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