Boundary integral equation methods for solving Laplace's equation with nonlinear boundary conditions: the smooth boundary case

Authors:
Kendall E. Atkinson and Graeme Chandler

Journal:
Math. Comp. **55** (1990), 451-472

MSC:
Primary 65N38; Secondary 65R20

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035924-X

MathSciNet review:
1035924

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Abstract: A nonlinear boundary value problem for Laplace's equation is solved numerically by using a reformulation as a nonlinear boundary integral equation. Two numerical methods are proposed and analyzed for discretizing the integral equation, both using product integration to approximate the singular integrals in the equation. The first method uses the product Simpson's rule, and the second is based on trigonometric interpolation. Iterative methods (including two-grid methods) for solving the resulting nonlinear systems are also discussed extensively. Numerical examples are included.

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DOI:
https://doi.org/10.1090/S0025-5718-1990-1035924-X

Article copyright:
© Copyright 1990
American Mathematical Society