Definite and Monotone Modified Trapezoidal Product Cubature Rules with A Posteriori Error Estimates

The authors introduce two modified trapezoidal product cubature rules, S-n and S+n, that provide one-sided approximations to double integrals over the square domain [a,b]2 for integrands from the class C2,2[a,b]. They prove monotonicity and derive a posteriori error estimates for the remainders of these cubature rules.