Related papers: Recent Symbolic Summation Methods to Solve Coupled…
We extend several celebrated methods in classical analysis for summing series of complex numbers to series of complex matrices. These include the summation methods of Abel, Borel, Ces\'aro, Euler, Lambert, N\"orlund, and Mittag-Leffler,…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…
We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…
We propose and implement an algorithm for solving an overdetermined system of partial differential equations in one unknown. Our approach relies on Bour-Mayer method to determine compatibility conditions via Jacobi-Mayer brackets. We solve…
The sparse difference resultant introduced in \citep{gao-2015} is a basic concept in difference elimination theory. In this paper, we show that the sparse difference resultant of a generic Laurent transformally essential system can be…
The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the…
A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conj unction of a finite number…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are based on suitable combinations of existing schemes for the…