Computation of an infinite integral using Romberg's method
The integral \[ g(a)= \int^t_0 [(\exp^x+ \exp^{-x})^a- \exp^{ax}- \exp^{-ax}]\,dx,\quad 0< a< 2 \] arises in a study of the total energy of crystals, where \(g(5/3)\) has been evaluated as 4.45. The aim of this paper is to show that a classical numerical computation, in this case with Romberg's method, leads to efficient and reliable computed results for any value of \(a\) if dynamical controls are used from the round-off error point of view. An estimation of the final round-off error and numerical examples are given.
scientific article; zbMATH DE number 2128418