The equivalence of several initial value methods for solving integral equations

✍ Scribed by Michael A. Golberg

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 224 KB
• Volume: 6
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(72)80022-9

✦ Synopsis

solutions to a class of Fredholm integral equations based on reducing the integral equation to an initial-value problem for a pair of integro-differential equations. On discretizing these equations one is led to a numerical procedure based on integrating a Cauchy problem for a finite system of ordinary differential equations. The question immediately arises as to whether the approximate solution obtained in this fashion differs from the solution obtained by solving a related set of linear algebraic equations. It is the purpose of this paper to establish the equivalence of the two methods. In particular we see that Kalaba's intial-value method converges whenever an associated method based on algebraic equations converges.