Some Computational Aspects of the Boundary Collocation Method for Linear Partial Differential Equations and Related Questions

摘要

Numerical properties of the boundary collocation method in applied mathematics are summarized. The determination of boundary collocation points for solving some problems for the Laplace operator is discussed. Polynomial approximation in the complex plane with applications to conformal mapping is considered along with some computational aspects of rational approximation in the complex plane. Solving an interface problem for the Laplace operator by the boundary collocation method and a fast method for solving certain integral equations of the first kind with application to conformal mappings are treated. A numerical method for analytic continuation of conformal mappings is also mentioned.