Related papers: Time-Spectral Efficiency
A stability analysis of the Borel-Laplace series summation technique, used as explicit time integrator, is carried out. Its numerical performance on stiff and non-stiff problems is analyzed. Applications to ordinary and partial differential…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to…
This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
In this paper, we develop a linearized fractional Crank-Nicolson-Galerkin FEM for Kirchhoff type quasilinear time-fractional integro-differential equation $\left(\mathcal{D}^{\alpha}\right)$. In general, the solutions to the time-fractional…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying…
We present a framework for solving time-dependent partial differential equations (PDEs) in the spirit of the random feature method. The numerical solution is constructed using a space-time partition of unity and random feature functions.…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
Energy-efficient real-time task scheduling has been actively explored in the past decade. Different from the past work, this paper considers schedulability conditions for stochastic real-time tasks. A schedulability condition is first…
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying…
This article offers sharp spatial and temporal mean-square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infinite dimensional fractional Brownian motion with the Hurst…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…
We apply the ultraspherical spectral method to solving time-dependent PDEs by proposing two approaches to discretization based on the method of lines and show that these approaches produce approximately same results. We analyze the…