(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
We present a new composite quadrature rule which is exact for polynomials of degree 2N+K-1 with N abscissas at each subinterval and K boundary conditions. The corresponding orthogonal polynomials are introduced and the analytic formulae for abscissas and weight functions are presented. Numerical results show that the new quadrature rule is more efficient, compared with classical ones.