Several error inequalities for a quadrature formula with a parameter and applications

AbstractIn this paper, we will derive several error inequalities for a quadrature formula with a parameter, which will not only provide some generalizations of the known results, but also give some other interesting quadrature formulae as special cases. Furthermore, sharp upper and lower error bounds for the double error inequalities are obtained. Applications in numerical integration are also given

The exponentially convergent trapezoidal rule

It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators

Guidance, flight mechanics and trajectory optimization. Volume 6 - The N-body problem and special perturbation techniques

Analytical formulations and numerical integration methods for many body problem and special perturbative technique

Unified inequalities of the q-Trapezium-Jensen-Mercer type that incorporate majorization theory with applications

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of ${\mathfrak{q}}$-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the $_{{\varsigma_{1}}}{\mathfrak{q}}$ and $^{{{\varsigma_{2}}}}{\mathfrak{q}}$ differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint ${\mathfrak{q}}$-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations

Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python

Numerical simulations; programming; Pytho

Programming for Computations - Python

Mathematics; Computer mathematics; Numerical analysis; Computer software; Numerical analysi