Modern Potential Theory And Its Applications In Numercal Computing

Modern potential theory has been widely applied to numerical computations in sciences and technology. This paper reviews part of the modern potential theory, which is related to numerical approximation, and discusses its application in numeircal computations, especially in the Gauss quadrature formula algorithm.Chapter 1 briefly introduces the background of modern potential theory. Chapter 2 introduces the essentials of the modern potential theory such as measures, potential energy, Fekete points, Gauss-Lobatto points and integral formula. Chapter 3 discusses its applications in numerical computations, which covers error estimates, configuration of interpolation points, convergence in measure and in capacity, and presents some examples. Chapter 4 is the new work on Gauss-quadrature formula, where we discuss the algorithms in the paper of Eslahch etc, "On numerical improvement of Gauss-Lobatto Quadrature rules". We correct some problems in their algorithms and offer a new algorithm, and give a concrete example to illustrate the reasonability of our algorithm. Chapter 5 gives summary and proposes the further research.