Toward better numerical integration

Romberg's quadrature is investigated with special emphasis on its use in automatic integration. Section 1 reproduces many of the facts known about Romberg's method and investigates the selection of stepsize. Section 2 discusses the integration of singular integrands, with emphasis on detecting algebraic endpoint singularities and the reliability of methods used for handling them. Section 3 looks at CADRE, the first automatic integration routine published based on the adaptive use of Romberg's method. It is adapted for use on the IBM 360 and is compared to SQUANK, an adaptive Simpson routine already available in the U.B.C. program library.Science, Faculty ofComputer Science, Department ofGraduat