Integral equation from an amateur's standpoint: technical memorandum - Morel-Seytoux, Hubert J., author; Colorado State University, publisher (Colorado State University. Libraries, 1965)
Methods of solution of linear integral equations are described. Methods are compared and ranked with respect to the ease with which they can yield exact analytical solutions in closed form. It is concluded that methods based on transform theory are most efficient. The transform method uses the transform property of the kernel operation itself, or that of an external transform operator, e .g., Laplace's transform. In the latter case the integral equation is Laplace-transformed, whereas in the former case the equation is "kernel"-transformed. The kernel-transform procedure yields immediate result whenever the nth-iterated kernel operator is expressible as a linear combination of lower order iterated kernel operators. The Laplace transform method yields immediate results whenever the integral in the equation is a convolution of the kernel and the unknown function. Generalizations are possible.
CER65HJM-76.
March 8, 1965.
Keywords: Integral equations