A New Composite Quadrature Rule (Advances in Applied Mathematics and Mechanics, 2021)
We present a new composite quadrature rule which is exact forpolynomials of degree $2N+K-1$ with $N$ abscissas at eachsubinterval and $K$ boundary conditions. The correspondingorthogonal polynomials are introduced and the analytic formulae forabscissas and weight functions are presented. Numerical results showthat the new quadrature rule is more efficient, compared withclassical ones.