Related papers: On the Stability of Exponential Integrators for No…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…
We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci.,…
We introduce exponential numerical integration methods for stiff stochastic dynamical systems of the form $d\mathbf{z}_t = L(t)\mathbf{z}_tdt + \mathbf{f}(t)dt + Q(t)d\mathbf{W}_t$. We consider the setting of time-varying operators $L(t),…
A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDEs) driven by space-time noise, for multiplicative and additive noise. We examine convergence of…
We consider the nonlinear Schr\"odinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class $W^{\alpha,2}$ for some $\alpha\in (0,1)$. Due to the loss of…
The inelastic incompressibility is a typical feature of metal plasticity/viscoplasticity. Over the last decade, there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
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…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…