A new computerizable quadrature formula using probabilistic approach

摘要

A new quadrature formula has been proposed which uses weight functions derived from a new probabilistic approach. Unlike the complicatedly structured quadrature formulae of Gauss, Hermite and others of similar type, the proposed quadrature formula only needs the values of integrand at user-defined equidistant points in the interval of integration and weight functions are not constants. The quadrature formula has been compared empirically with two other simple fundamental methods of integration. The percentage relative gain in efficiency of the quadrature formula with respect to fundamental methods of integration has been computed for certain selected functions and with different number of node points in the interval of integration. It has been observed that the proposed quadrature formula produces significantly better results than the other simple fundamental methods of integration.