Related papers: Semi-implicit-explicit Runge-Kutta method for nonl…
One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity…
The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed…
We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach fully…
We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge--Kutta--Legendre (RKL) and Runge--Kutta--Gegenbauer (RKG) super-time-stepping methods were…
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…
We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step…
We consider the efficient numerical solution of coupled dynamical systems, consisting of a small nonlinear part and a large linear time invariant part, possibly stemming from spatial discretization of an underlying partial differential…
The convergence of a family of AMF-Runge-Kutta methods (in short AMF-RK) for the time integration of evolutionary Partial Differential Equations (PDEs) of Advection Diffusion Reaction type semi-discretized in space is considered. The…
In this paper, two novel classes of implicit exponential Runge-Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, we analyze the symplectic conditions of two kinds of exponential integrators, and present a…
We discuss Implicit-Explicit (IMEX) Runge Kutta methods which are particularly adapted to stiff kinetic equations of Boltzmann type. We consider both the case of easy invertible collision operators and the challenging case of Boltzmann…
Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a…
The main objective of this series of papers is to explore the entire landscape of numerical methods for fast nonlinear Fourier transformation (NFT) within the class of integrators known as the exponential integrators. In this paper, we…
We present a novel and general methodology for building second-order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two-dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second-order…
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some…
In this work, an approximate family of implicit multiderivative Runge-Kutta (MDRK) time integrators for stiff initial value problems is presented. The approximation procedure is based on the recent Approximate Implicit Taylor method (Baeza…
Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient numerical methods. Exponential integrators have recently…
Implicit-Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is partitioned into stiff and nonstiff processes with the goal of lower computational costs than a purely…