In this paper, an iterative numerical method for obtaining approximate values of
definite single, double and triple integrals will be illustrated. This method depends on
approximating the single integral function by spline polynomial of fifth degre
e, while
Gauss Legendre points as well as spline polynomials are used for finding multiple
integrals.
The study shows that when the method are applied to single integrals is convergent
of order sixth, as well as when applied to triple integrals is convergent of order sixth for
three Gauss Legendre points or greater.
Errors estimates of the proposed method alongside numerical examples are given to
test the convergence and accuracy of the method.
