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Integral Equations

S. Richardson
Journal / Anthology

The Mathematica Journal
Year: 2004
Volume: 9
Issue: 2
Page range: 360-482

Introductory Example; The Condenser Problem; Conformal Mapping; Nekrasov's Equation; Concluding Remarks; References

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.

*Mathematics > Calculus and Analysis
*Science > Physics > Fluid Mechanics