Numerical Solution Of The Laplace Equation Types Of Internal And External Problems

In this paper, the Laplace's equation with various boundary value problems are discussed by using potential theory, and numerical solutions and examples are given. There are six main parts in this paper:1. This chapter describes the research situation and important role of the Laplace equation, including basic knowledge, potential theory and Nystrom method.2. The four operators of Laplace's equation are deduced in detail, especially for the hypersingular operator.3. The open arc problem with the Dirichlet boundary value problem is stud-ied, and the numerical solution and examples are given to show the effectiveness of the method mentioned above.4. The exterior Neumann boundary value problem is studied, and the nu-merical solution and examples are given to show the effectiveness of the method mentioned above.5. The interior and exterior Robin problems are discussed by using single and double potential, and the numerical solution and typical examples are given to show the effectiveness of the method mentioned above.6. The transmission problem is studied by using single-layer potential, and a numerical solution and examples are given.