Related papers: Novel Numerical Algorithm with Fourth-Order Accura…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation where the parabolicity condition is allowed to degenerate. Such…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…
In this paper, we investigate a spectral Petrov-Galerkin method for fractional initial value problems. Singularities of the solution at the origin inherited from the weakly singular kernel of the fractional derivative are considered, and…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
We propose a block finite difference, error inhibiting scheme that is fourth-order accurate for short to moderate times and has a six-order convergence rate for long times. This scheme outperforms the standard fourth-order Finite Difference…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference method. Typically, when free boundary problems are solved…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the…
The Schwarzian-Newton method can be defined as the minimal method for solving nonlinear equations $f(x)=0$ which is exact for any function $f$ with constant Schwarzian derivative; exactness means that the method gives the exact root in one…
In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a…
We present an arbitrary order discontinuous Galerkin finite element method for solving the fourth-order curl problem using a reconstructed discontinuous approximation method. It is based on an arbitrarily high-order approximation space with…
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…