Asymptotically optimal definite quadrature formulae of $4$-th order
Provides new explicit quadrature formulae with proven optimality for numerical integration, benefiting researchers in numerical analysis.
The paper constructs sequences of asymptotically optimal definite quadrature formulae of fourth order with explicit weights and nodes, and evaluates their error constants. It establishes monotonicity properties for 4-convex functions and provides a-posteriori error estimates.
We construct several sequences of asymptotically optimal definite quadrature formulae of fourth order and evaluate their error constants. Besides the asymptotical optimality, an advantage of our quadrature formulae is the explicit form of their weights and nodes. For the remainders of our quadrature formulae monotonicity properties are established when the integrand is a 4-convex function, and a-posteriori error estimates are proven.