some applications of sigmoid functions

In numerical analysis, the process of fitting a function via given data is called interpolation. interpolation has many applications in engineering and science. there are several formal kinds of interpolation, including linear interpolation, polynomial interpolation, piecewise constant interpolation, trigonometric interpolation, and so on. in this article, by using sigmoid functions, a new type of interpolation formula is presented. to illustrate the efficiency of the proposed new interpolation formulas, some ap plications in quadrature formulas (in both open and closed types), numerical integration for double integral, and numerical solution of an ordinary differential equation are included. the advantage of this new approach is shown in the numerical applications section.