Related papers: An improved high order finite difference method fo…
This paper establishes an existence theory for discrete second-order boundary value problems on non-uniform time grids using the upper and lower solution method. We consider difference equations of the form $u^{\Delta\Delta}(t_{i-1}) +…
In this paper we establish a stability barrier of a class of high-order Hermite-type discretization of 1D advection equations underlying the hybrid-variable (HV) and active flux (AF) methods. These methods seek numerical approximations to…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid…
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…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
Based on our recent results, in this paper, a compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions. The proposed scheme is second order accurate in time and…
We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…
Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute…
In this paper, we propose a new virtual interpolation point method to formulate the discrete Stokes equations. We form virtual staggered structure for the velocity and pressure from the actual computation node set. The virtual interpolation…
We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily…
We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We…
In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we…
In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
We develop summation by parts (SBP) approach for generating high-order finite-difference schemes on the interval and propose new sets of schemes up to the 12th order. The coefficients of the schemes are governed by values of grid spacing…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…