相关论文: Recent Symbolic Summation Methods to Solve Coupled…

Methods of determining, from small-variable asymptotic expansions, the characteristic exponents for variables tending to infinity are analyzed. The following methods are considered: diff-log Pad\'e summation, self-similar factor…

This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…

Transseries expansions build upon ordinary power series methods by including additional basis elements such as exponentials and logarithms. Alternative summation methods can then be used to "resum" series to obtain more efficient…

Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable…

By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in…

This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit…

The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…

The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…

In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly-valid asymptotic solutions to autonomous and non-autonomous difference equations in the neighbourhood of a…

This paper is devoted to the study of infinitesimal limit cycles that can bifurcate from zero-Hopf equilibria of differential systems based on the averaging method. We develop an efficient symbolic program using Maple for computing the…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…

We propose a linear algorithm for determining two function parameters by their linear combination. These functions must satisfy the first order differential equations with polynomial coefficients and our parameters are the coefficients of…

This work focuses on developing high-order energy-stable schemes for wave-dominated problems in closed domains using staggered finite-difference summation-by-parts (SBP FD) operators. We extend the previously presented uniform staggered…

Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and…

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…

In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…

The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…