Product integration rules by the constrained mock-Chebyshev least squares operator

Abstract In this paper we consider the problem of approximation definite integrals on finite intervals for integrand functions showing some kind “pathological” behavior, e.g. “nearly” singular functions, highly oscillating weakly etc. particular, introduce and study a product rule based equally spaced nodes constrained mock-Chebyshev least squares operator. Like other polynomial or rational methods, operator was recently introduced in order to defeat Runge phenomenon that occurs when using interpolation large sets points. Unlike methods piecewise mainly used case nodes, our offers high efficiency, with performances slightly lower than those global orthogonal polynomials same spaces functions. We convergence provide error estimates subspaces continuous test effectiveness formula by means several examples, which confirm theoretical estimates.