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.


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


Full Text: DOI


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