Related papers: A second-order exponential time differencing schem…
It is well known that the exponential time differencing (ETD) method has been successfully applied to the classic Cahn-Hilliard equation with double well potential. However, this numerical method can not be extended to the Cahn-Hilliard…
The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it is used to construct difference schemes generating…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…
The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential…
Emphatic temporal difference (ETD) learning (Sutton et al., 2016) is a successful method to conduct the off-policy value function evaluation with function approximation. Although ETD has been shown to converge asymptotically to a desirable…
Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires…
Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face significant image quality…
In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional It\^o diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or…
In this paper, we study high-order exponential time differencing Runge-Kutta (ETD-RK) discontinuous Galerkin (DG) methods for nonlinear degenerate parabolic equations. This class of equations exhibits hyperbolic behavior in degenerate…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
The nonlocal Allen-Cahn (NAC) equation is a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion operator, and satisfies the maximum principle as its local counterpart. In this…
We construct, analyse and assess various schemes of second order of accuracy in space and time for model advection-diffusion-reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial…
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and…
We provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…