Isomeric trees and the order of Runge--Kutta methods

Classés selon la proximité de leur titre et de leur résumé avec ceux de cet article. Sélectionnez-en pour les lire ensemble.

Les articles les plus proches

1. Apparenté Pas pertinent

   Solving Backward Doubly Stochastic Differential Equations through Splitting Schemes

   Feng Bao, Yanzhao Cao, He Zhang · 2021 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic differential equation. The backward stochastic differential equation and the stochastic differential equation are then approximated by first order finite difference schemes, which results in a first order scheme for the backward doubly stochastic differential equation. Numerical experiments are conducted to illustrate the convergence rate of the proposed scheme.

2. Apparenté Pas pertinent

   Certified homotopy tracking using the Krawczyk method

   Timothy Duff, Kisun Lee · 2024 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   We revisit the problem of certifying the correctness of approximate solution paths computed by numerical homotopy continuation methods. We propose a conceptually simple approach based on a parametric variant of the Krawczyk method from interval arithmetic. Unlike most previous methods for certified path-tracking, our approach is applicable in the general setting of parameter homotopies commonly used to solve polynomial systems of equations. We also describe a novel preconditioning strategy and give theoretical correctness and termination results. Experiments using a preliminary implementation of the method indicate that our approach is competitive with specialized methods appearing previousl…

3. Apparenté Pas pertinent

   Fractional Newton-Raphson Method

   A. Torres-Hernandez, F. Brambila-Paz · 2017 · Applied Mathematics and Sciences: An International Journal (MathSJ), 8:1-13, 2021 · Pas encore résumé

   Résumé scientifique

   The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.

4. Apparenté Pas pertinent

   Generalising the Fast Reciprocal Square Root Algorithm

   Mike Day · 2023 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer instructions, and second, the coarse result is refined through one or more steps, traditionally using Newtonian iteration but alternatively using improved expressions with carefully chosen numerical constants found by other authors. The algorithm was widely used before microprocessors carried built-in hardware support for computing reciprocal square roots. At the time of writing, however, there is in general no hardware acceleration for computing other fixed frac…

5. Apparenté Pas pertinent

   A robust solution strategy for the Cahn-Larché equations

   Erlend Storvik, Jakub Wiktor Both, Jan Martin Nordbotten et al. · 2022 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be seen as a combination of the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-linearly coupled, has a fourth order term that comes from the Cahn-Hilliard subsystem, and is non-convex and nonlinear in both the phase-field and displacement variables. We propose a novel semi-implicit discretization in time that uses a standard convex-concave splitting method of the nonlinear double-well potential, as well as special treatment…

6. Apparenté Pas pertinent

   The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems

   Matthew J. Colbrook · 2022 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. However, Koopman operators are infinite-dimensional, and computing their spectral information is a considerable challenge. We introduce measure-preserving extended dynamic mode decomposition ($\texttt{mpEDMD}$), the first truncation method whose eigendecomposition converges to the spectral quantities of Koopman operators for general measure-preserving dynamical systems. $\texttt{mpEDMD}$ is a data-driven algorithm based on an orthogonal Procrustes problem that enforces measure-preserving truncations of Koopman op…

7. Apparenté Pas pertinent

   Compatible finite element methods for geophysical fluid dynamics

   Colin J. Cotter · 2023 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces which are linked by the operators of differential calculus. The use of discrete de Rham complexes to solve partial differential equations is well established, but in this article we focus on the specifics of dynamical cores for simulating weather, oceans and climate. The most important consequence of the discrete de Rham complex is the Hodge-Helmholtz d…

8. Apparenté Pas pertinent

   Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular Solutions

   Gilles Chardon, Laurent Daudet · 2013 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the Finite Element Method, at reduced complexity, and with large flexibility in the implementation choices.