Related papers: A Spherical Crank-Nicolson Integrator Based on the…
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions…
We consider a time-stepping scheme of Crank-Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step…
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation with a strong inhomogeneous magnetic…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
We present a class of exponential integrators to compute solutions of the stochastic Schr\"odinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the…
In this paper, we present an implicit Crank-Nicolson finite element (FE) scheme for solving a nonlinear Schr\"odinger-type system, which includes Schr\"odinger-Helmholz system and Schr\"odinger-Poisson system. In our numerical scheme, we…
This paper proposes and analyzes a finite difference method based on compact schemes for the Euler-Bernoulli beam equation with damping terms. The method achieves fourth-order accuracy in space and second-order accuracy in time, while…
The paper is devoted to a constitutive solution, limit load analysis and Newton-like methods in elastoplastic problems containing the Mohr-Coulomb yield criterion. Within the constitutive problem, we introduce a self-contained derivation of…
In this paper we continue the work on implicit-explicit (IMEX) time discretizations for the incompressible Oseen equations that we started in \cite{BGG23} (E. Burman, D. Garg, J. Guzm\`an, {\emph{Implicit-explicit time discretization for…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A…
We present high-order, fully explicit projective integration schemes for nonlinear collisional kinetic equations such as the BGK and Boltzmann equation. The methods first take a few small (inner) steps with a simple, explicit method (such…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
In this paper, we present a novel numerical scheme for simulating deformable and extensible capsules suspended in a Stokesian fluid. The main feature of our scheme is a partition-of-unity (POU) based representation of the surface that…