Uniform algebraic hyperbolic spline quasi‐interpolant based on mean integral values

In the present work, a novel spline quasi-interpolation operator reproducing both constant polynomials and algebraic hyperbolic functions is presented. The quasi-interpolant to a given function is defined from the integrals on every interval of the function to be approximated. Compared to the other existing methods, this operator does not need any additional end conditions and it is easy to be implemented without solving any system of equations. The approximation properties of the operator are theoretically analyzed and some numerical tests are presented to illustrate its performance.