Related papers: An Accurate and Efficient Algorithm for The Time-f…
Over the past few years it has been demonstrated that "coarse timesteppers" establish a link between traditional numerical analysis and microscopic/ stochastic simulation. The underlying assumption of the associated…
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly…
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In…
Purpose -- RF circuits often possess a multi-rate behavior. Slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit. Frequency modulated signals pose a particular challenge.…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…
The subdiffusion equation with a Caputo fractional derivative of order $\alpha\in(0,1)$ in time arises in a wide variety of practical applications, and it is often adopted to model anomalous subdiffusion processes in heterogeneous media.…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely q-homotopy analysis transform method. These equations are playing a…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
Real-time dispatch practices for operating the electric grid in an economic and reliable manner are evolving to accommodate higher levels of renewable energy generation. In particular, stochastic optimization is receiving increased…
In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit…