Date of Award
5-1965
Degree Type
Report
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
Committee Chair(s)
Wendell L. Pope
Committee
Wendell L. Pope
Abstract
An integral equation of the form
ζ(x) - λ∫ K(x, s) ζ(s) ds = f(x) a ≤ x ≤ b
is called a Fredholm equation. By the method of successive approximations a solution can be obtained if the parameter λ is sufficiently small. If the kernel, K (x, s), is degenerate then a solution can be obtained by reducing it to a system of linear algebraic equations. In the general case the kernel is represented as an infinite Fourier Series. With this representation the solution is obtained by combining the two methods mentioned. The solution is the solution of two integral equations, one of which is solvable by successive approximations and the other has a degenerate kernel. The conditions for solvability of the Fredholm equations will be proven.
Recommended Citation
Furness, Dewey F., "Fredholm Solution of Linear Integral Equations" (1965). All Graduate Plan B and other Reports, Spring 1920 to Spring 2023. 1120.
https://digitalcommons.usu.edu/gradreports/1120
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