Improving the accuracy of multiple integral evaluation by applying Romberg’s method

Romberg’s method, which is used to improve the accuracy of one-dimensional integral evaluation, is extended to multiple integrals if they are evaluated using the product of composite quadrature formulas. Under certain conditions, the coefficients of the Romberg formula are independent of the integral’s multiplicity, which makes it possible to use a simple evaluation algorithm developed for one-dimensional integrals. As examples, integrals of multiplicity two to six are evaluated by Romberg’s method and the results are compared with other methods.