The majority of computer algebra systems (CAS) support symbolic integration using a combination heuristic algebraic and rule-based (integration table) methods. In this paper, we present hybrid (symbolic-numeric) method to calculate the indefinite integrals univariate expressions. Our is broadly similar Risch-Norman algorithm. primary motivation for work add functionality modern CAS (the manipul...

We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of ill-conditioning to which numerical methods are susceptible. We propose two alternative methods for exact input that compute the rational part of the integral using He...

The impulse sources are heat impulses or force impulses lengthways the arrangements. They are represented mathematically by Delta functions and Dirac impulses of finite duration. Conventional fitting conditions are compared hereby. The successive time integration of the PDE provides a system of two equations. A Dirac impulse changes into a Ramp function this way and the Delta function becomes t...

This study targets the behavior of shear buildings equipped with tuned liquid column dampers (TLCD) which attenuate dynamic load-induced vibrations. TLCDs are a passive damping system used in tall buildings. This kind of damper has proven to be very efficient, being an excellent alternative to mass dampers. A dynamic analysis of the structure-damper system was made using the software DynaPy, de...

2 Numerical and Symbolic Integration 2 2.1 Cubature Formulae Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Constructing Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.1 Interpolatory Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.2 Ideal Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://www.ski.org/gofen/TaylorMethod.htm) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D ...

Output-feedback high-order sliding-mode (HOSM) controls include HOSM-based differentiators and, therefore, possess complicated discontinuous dynamics. Their practical application naturally involves discrete noisy output sampling and numeric integration of the internal variables. Resulting hybrid systems are shown to be stable, and the corresponding asymptotic sliding-mode accuracies are calcula...