Publication Date
7-18-1973
Abstract
This dissertation first develops a method for solving the integral equation when y(z') is a constant and then extends it to the case where y(z') is a step function. The solution of the integral equation is achieved by solving the integro differential invariant imbedding equations derived from the integral equation by varying the limits of integration. The imbedding equations are solved using a moment method which reduces the calculation to an initial value problem. Proofs of the existence and convergence of the method are given. In the case where y(z') is a constant, the solution of the integral equation is obtained by a simple quadrature of the product of the solution with a transform of the function g(z). In the case where y(z') is a step function, the integro differential equations for the reflection and transmission kernels are reduced to initial value problems and solved. These kernels are used to obtain fluxes from which the solution to the integral equation can again be obtained by simple quadratures.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Richard Crenshaw Allen
Second Committee Member
Liang-Shin Hahn
Third Committee Member
Steven Arthur Pruess
Fourth Committee Member
Donald Ward Dubois
Language
English
Document Type
Dissertation
Recommended Citation
Boicourt, Grenfell Paul. "A Method Of Moments Applied To An Invariant Imbedding Solution Of A Certain Class Of Fredholm Integral Equations.." (1973). https://digitalrepository.unm.edu/math_etds/217
