Related papers: Dual Algorithms
In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the convective fluxes are split into positive and negative parts,…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
This paper proposes a Direct Rational Radial Basis Functions Partition of Unity (D-RRBF-PU) approach to compute derivatives of functions with steep gradients or discontinuities. The novelty of the method concerns how derivatives are…
This paper proposes a methodology to calculate both the first and second derivatives of a vector function of one variable in a single computation step. The method is based on the nested application of the dual number approach for first…
Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient numerical methods. Exponential integrators have recently…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated…
In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the…
The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Gaussian, multiquadric, Matern and thin-plate splines, in one…
Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast and slow variables can be linearly separated using additive or…
This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system.…
This paper applies meshless method of lines, which uses radial basis functions (RBFs) as a spatial collocation scheme to solve the Coupled Drinfeld's-Sokolov-Wilson System. Runge-Kutta method is used for time integration of the system of…
Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate…
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in [8]. These specially designed methods use reduced precision or the implicit computations and full…
Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit…
A semi-implicit-explicit (semi-IMEX) Runge-Kutta (RK) method is proposed for the numerical integration of ordinary differential equations (ODEs) of the form $\mathbf{u}' = \mathbf{f}(t,\mathbf{u}) + G(t,\mathbf{u}) \mathbf{u}$, where…
In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
This article studies a direct numerical approach for fractional advection-diffusion equations (ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential quadrature (DQ) method is firstly proposed for the 1D and…
This paper presents a class of Crank-Nicolson (CN) type schemes enhanced by radial basis function (RBF) interpolation for the time integration of linear parabolic partial differential equations (PDEs). The resulting RBF-CN schemes preserve…