Related papers: Algorithm to find an all-order in the running coup…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
We formulate and numerically solve the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi~(DGLAP) evolution equations at next-to-leading order in perturbation theory directly for a basis of 6 physical, observable structure functions in deeply…
In this letter we apply a method recently devised in \cite{aapla03} to find precise approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in \cite{aapla03} is refined and results of much…
We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals of motion associated with the given…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
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…
In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…
We develop a search algorithm for systems of $q$-difference equations satisfied by Andrews-Gordon type double series. We then couple the search algorithm with Euler's algorithm for finding infinite products to narrow the search space. We…
We devise the first constant-factor approximation algorithm for finding an integral multi-commodity flow of maximum total value for instances where the supply graph together with the demand edges can be embedded on an orientable surface of…
We present a new general algorithm for calculating arbitrary jet cross sections in arbitrary scattering processes to next-to-leading accuracy in perturbative QCD. The algorithm is based on the subtraction method. The key ingredients are new…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
Polarised singlet DGLAP equations are solved by applying the method of characteristics. The singlet equations are first transformed into a pair of coupled partial differential equations by a Taylor series expansion valid to be at small x.…
We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…
A generalization of the leading-order DGLAP evolution at small x is performed for the non-singlet structure function by resumming the leading-order DGLAP anomalous dimension to all orders in the QCD coupling. Explicit expressions are…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
A discretization scheme for variable coefficient elliptic PDEs in the plane is presented. The scheme is based on high-order Gaussian quadratures and is designed for problems with smooth solutions, such as scattering problems involving soft…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…