Related papers: Unconditional Stability for Multistep ImEx Schemes…
The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to…
We propose an explicit partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed to achieve high computational efficiency in modern engineering simulations. The FSI problem under…
In this paper, we construct and analyze new first- and second-order implicit-explicit (IMEX) schemes for the unsteady Navier-Stokes-Darcy model to describe the coupled free flow-porous media system, which is based on the scalar auxiliary…
Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…
Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…
We propose a novel flexible-step model predictive control algorithm for unknown linear time-invariant discrete-time systems. The goal is to asymptotically stabilize the system without relying on a pre-collected dataset that describes its…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
This paper considers a two-step fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving the time-variable fractional mobile-immobile advection-dispersion model subjects to suitable initial and boundary conditions.…
High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dynamical behaviors. While several high-order implicit-explicit…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
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…
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and…
In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions…
We study the problem of global exponential stabilization of a force- and torque-controlled unicycle model in discrete time. To this end, we extend a recently introduced approach to model predictive control (MPC) in which a flexible number…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…