Convergence of Numerical Solution of Generalized Theodorsen’s Nonlinear Integral Equation

Abstract

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.