Urevc, Janez Rus, Primož Halilovič, Miroslav

V tem delu je predstavljen nov razred metod tipa Runge-Kutta (RK) za numerično reševanje navadnih diferencialnih enačb (NDE). V primerjavi s klasičnimi metodami RK izpeljava metod temelji na uteženi integralni obliki NDE. Pristop omogoča povečanje natančnosti uveljavljenih kolokacijskih metod tipa RK ob ohranjanju enakega števila stopenj metode (t....

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Naglič, Andraž

Delo obravnava pristope k numeričnem integriranju funkcij več spremenljivk. Opisani pristopi so uporaba kvadraturnih formul, reševanje sistema polinomskih enačb in verjetnostna metoda Monte Carlo. Glavni del naloge obravnava konstrukcijo formul s pozitivnimi utežmi. Izpeljane so meje za število vozlov teh formul in sistemi enačb, s katerimi dobimo ...

Vysotsky, L. I. Smirnov, A. V. Tyrtyshnikov, E. E.
Published in
Lobachevskii Journal of Mathematics

AbstractNumerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to overcome this problem. Tensor-train decomposition of a tensor approximating the integrand is constructed...

Turner, James Paul Nowotny, Thomas
Published in
Frontiers in Neuroinformatics

Motivated by the challenge of investigating the reproducibility of spiking neural network simulations, we have developed the Arpra library: an open source C library for arbitrary precision range analysis based on the mixed Interval Arithmetic (IA)/Affine Arithmetic (AA) method. Arpra builds on this method by implementing a novel mixed trimmed IA/AA...

timofejeva, inga navickas, zenonas telksnys, tadas marcinkevicius, romas ragulskis, minvydas

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is con...

bourgiotis, sotiris frangos, panayiotis sautbekov, seil pshikov, mustakhim

A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lo...

Radhia, Bessi

Function approximations arises in many branches of applied mathematics and computer science, in particular in numerical analysis, in finite element theory and more recently in data sciences domain. From most common approximation we cite, polynomial, Chebychev and Fourier series approximations. In this work we establish some approximations of a cont...

brehm, martin thomas, martin

We present a novel method for the computation of well-defined optimized atomic partial charges and radii from the total electron density. Our method is based on a two-step radical Voronoi tessellation of the (possibly periodic) system and subsequent integration of the total electron density within each Voronoi cell. First, the total electron densit...