相关论文: Numerical computation of real or complex elliptic …

We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…

The numerical simulation of the 3D incompressible Euler equation is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two…

An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…

By considering an empirical approximation, and a new class of operators that we will call walking operators, we construct, for any positive ND-toeplitz matrix, an infinite in all dimensions matrix, for which the inverse approximates the…

Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…

This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.

Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The recursion formulas for these sums are derived, which are easily…

Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and…

An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…

We enumerate total cyclic orders on $\left\{1,\ldots,n\right\}$ where we prescribe the relative cyclic order of consecutive triples $(i,{i+1},{i+2})$, these integers being taken modulo $n$. In some cases, the problem reduces to the…

We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…

Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…

We show that the use of generalized multivariable forms of Hermite polynomials provide an useful tool for the evaluation of families of elliptic type integrals often encountered in electrostatic and electrodynamics

We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…

This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…

Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…

The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…

Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to…