#### 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

#### Recommended Citation

Russell, Robert Dodd. "I. Existence of Eigenvalues for Integral Equations; II. A Collocation Method for Boundary Value Problems." (1970). https://digitalrepository.unm.edu/math_etds/144