A new proof of the Euler-Maclaurin expansion for quadrature over implicitly defined curves
This paper provides a short proof of the existence of an expansion in even powers of the grid parameter \(h\) for the error in a remarkable simple integraton rule for line integrals. The integration rule is a natural generalization of the trapezoidal rule. The generalized rule can be used for integration of a smooth \(n\)-dimensional vector-valued integrand along a smooth parameterized curve in \(n\) dimensions. The derivations given in the paper are based on the use of Taylor series combined with one-dimensional Euler-Maclaurin expansions.
scientific article; zbMATH DE number 1367880