相关论文: Implicit-explicit BDF $k$ SAV schemes for general …

Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising explicit schemes are associated with explicit-implicit…

We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…

Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue…

The phase field method is an effective tool for modeling microstructure evolution in materials. Many efficient implicit numerical solvers have been proposed for phase field simulations under uniform and time-invariant model parameters. We…

This is one of our series works on discrete energy analysis of the variable-step BDF schemes. In this part, we present stability and convergence analysis of the third-order BDF (BDF3) schemes with variable steps for linear diffusion…

In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…

Based on the equivalence of A-stability and G-stability, the energy technique of the six-step BDF method for the heat equation has been discussed in [Akrivis, Chen, Yu, Zhou, Math. Comp., Revised]. Unfortunately, this theory is hard to…

Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential…

In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction…

It is a very common practice to use semi-implicit schemes in various computations, which treat selected linear terms implicitly and the nonlinear terms explicitly. For phase-field equations, the principal elliptic operator is treated…

The Smectic-A (SmA) phase is modeled by a modified Landau-de Gennes (mLdG) model proposed by Xia et al. [Phys. Rev. Lett., 126 (2021), 177801], in which a tensor order parameter Q for the orientational order is coupled with a real scalar…

This paper develops a numerical procedure to accelerate the convergence of the Favre-averaged Non-Linear Harmonic (FNLH) method. The scheme provides a unified mathematical framework for solving the sparse linear systems formed by the mean…

Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to as flux differencing. We provide simple and efficient…

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate…

The classic second-order average vector field (AVF) method can exactly preserve the energy for Hamiltonian ordinary differential equations and partial differential equations. However, the AVF method inevitably leads to fully-implicit…

We consider numerical approximations and error analysis for the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (P. Knopf et. al., arXiv, 2020). Based on the stabilized linearly implicit approach, a…

Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain…

In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…

Many hyperbolic and kinetic equations contain a non-stiff convection/transport part and a stiff relaxation/collision part (characterized by the relaxation or mean free time $\varepsilon$). To solve this type of problems, implicit-explicit…

Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…