This paper is concerned with numerical integration over the unit square U 2 of continuous functions which are periodic in both variables. The concept of r-th order blending rectangle rule is introduced by carry
There is an aphorism in ancient China: “Golden corners, silvery edges, and strawy voids”. It means that the empty corner inside the box is the best place to be filled, then the boundary line of the empty space, and the void space is the worst. And more, if the Selecting rule ...
Finally, we present an innovative composite Levin quadrature rule for solving nearly singular and highly oscillatory problems. In contrast to existing numerical integration methods, the proposed composite method does not suffer from high oscillation and nearly singular amplitudes. Numerical tests included ...