Related papers: Explicit and implicit TVD schemes for conservation…
In this paper we carry out numerical analysis for a family of simplified gas transport models with hydrate formation and dissociation in subsurface, in equilibrium and non-equilibrium conditions. These models are adequate for simulation of…
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…
We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation…
We study the implicit upwind finite volume scheme for numerically approximating the linear continuity equation in the low regularity DiPerna-Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev…
We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately resolving the behavior of a solution whose derivatives are…
The discrete gradient structure and the positive definiteness of discrete fractional integrals or derivatives are fundamental to the numerical stability in long-time simulation of nonlinear integro-differential models. We build up a…
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in this setting that apply to piecewise smooth entropy…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…
Based on the popular Caputo fractional derivative of order $\beta$ in $(0,1)$, we define the censored fractional derivative on the positive half-line $\mathbb R_+$. This derivative proves to be the Feller generator of the censored (or…
A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint $\divb=0$ for the magnetic field vector $\bb$, is proposed. The…
Motivated by the statistical description of turbulence, we study statistical conservation laws in the form of kinetic-type PDEs for joint probability density functions (PDFs) and cumulative distribution functions (CDFs) associated with…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…
Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration…
In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an initial value problem (IVP) for the partial differential…
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation of the integral in the definition of the Caputo derivative.…
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…