We show how Mathematica can be used to obtain numerical solutions of integral equations by exploiting a combination of iteration and interpolation. The efficacy of the method is demonstrated by considering three classical integral equations of applied mathematics: Love's equation for the condenser problem, Theodorsen's equation associated with conformal mapping, and Nekrasov's equation arising in the theory of water waves. The success of the approach depends on the use of an appropriate method for the interpolation.
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Introductory Example
The Condenser Problem
Conformal Mapping
Nekrasov's Equation
Concluding Remarks
References


About the Author
Stan Richardson received his Ph.D. in applied mathematics from the University of Cambridge in 1968 and has been at Edinburgh since 1971. His principal research interest is in free boundary problems, particularly those arising in fluid mechanics, the approach being essentially analytic using methods based on conformal mapping and complex variable theory.
Stan RichardsonSchool of Mathematics University of Edinburgh James Clerk Maxwell Building The King' s Buildings Mayfield Road Edinburgh EH9 3JZ Scotland S.Richardson@ed.ac.uk
