Appropriate Algorithm for Assessment of Numerical Integration

In this paper, an appropriate algorithm for assessing numerical integration is proposed from a practical viewpoint, which takes “good lattice point” (GLP) and uniform design method as the basis. The analysis of spatial feature of a single peak function indicates that 11 uniform specimen points could give an estimation of the peak value of a cosine function with less error in one period range; furthermore, it shows that an appropriate assessment for the numerical integration of a function within its mono-modal domain can be gained with preliminary 11, 17 and 19 specimen points in one variable, two variables and three variables, respectively, provided the distribution of the discrete specimen points is uniform and deterministic in the domain in accordance with the rules of GLP and uniform design methodology; thereafter, several typical examples are presented to show the applicability of the new algorithm in conducting numerical integration for physical problems.