Date of Award
Master of Science (MS)
Mathematics and Statistics
Wendell L. Pope
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.
Furness, Dewey F., "Fredholm Solution of Linear Integral Equations" (1965). All Graduate Plan B and other Reports. 1120.
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