相关论文: Explicit and implicit TVD schemes for conservation…
Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…
A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it is firstly done that the original…
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical ($\alpha=1$) differential equation in the fractional case (here using fractional…
The subdiffusion equation with a Caputo fractional derivative of order $\alpha\in(0,1)$ in time arises in a wide variety of practical applications, and it is often adopted to model anomalous subdiffusion processes in heterogeneous media.…
In this paper we construct a new difference analog of the Caputo fractional derivative (called the $L2$-$1_\sigma$ formula). The basic properties of this difference operator are investigated and on its basis some difference schemes…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform…
In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (eventually with a positive corrective term at the righ-hand-side…
Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky system where the Caputo fractional derivative is of order $\alpha\in(1,2)$. We achieve such result for a suitable class of weak solutions.
The well-known Caputo fractional derivative and the corresponding Caputo fractional integral occur naturally in many equations that model physical phenomena under inhomogeneous media. The relationship between the two fractional terms can be…
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of…
We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is…
In this paper we extend the notion of an $\alpha$-family of maps to discrete systems defined by simple difference equations with the fractional Caputo difference operator. The equations considered are equivalent to maps with falling…
In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the…
We present an efficient algorithm for the evaluation of the Caputo fractional derivative $_0^C\!D_t^\alpha f(t)$ of order $\alpha\in (0,1)$, which can be expressed as a convolution of $f'(t)$ with the kernel $t^{-\alpha}$. The algorithm is…
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of…
Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…