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Convergence of numerical solution of generalized Theodorsen’s nonlinear integral equation. (English) Zbl 1470.65215

Summary: We consider a nonlinear integral equation which can be interpreted as a generalization of Theodorsen’s nonlinear integral equation. This equation arises in computing the conformal mapping between simply connected regions. We present a numerical method for solving the integral equation and prove the uniform convergence of the numerical solution to the exact solution. Numerical results are given for illustration.

MSC:

65R20 Numerical methods for integral equations
30C30 Schwarz-Christoffel-type mappings
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)

Software:

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References:

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