Gauss-Legendre-Radau and Gauss-Legendre-Lobatto Numerical Integration

Abstract

Gauss formulae for numerical integration are based on calculating the values of the integrand at Gaussian nodes and multiplying these values by weight factors, whereby the nodes are nonuniformly distributed in order to achieve higher accuracy compared to the uniform distribution of nodes. In this work Gauss-Legendre-Radau and Gauss-Legendre-Lobatto integration formulae, in which at least one end of the integration interval is a node, are listed in detail. These formulae are tested using the Runge function.