Related papers: $ hp $-version collocation method for a class of n…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…
We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our…
This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…
An $hp$-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the $hp$-version error estimates of two $L^2$ projection operators. Then incorporated…
This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit…
In this paper, we propose and study the asymptotic convergence and nonasymptotic global convergence rates (iteration-complexity) of an inertial under-relaxed version of the relative-error hybrid proximal extragradient (HPE) method for…
This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
In this paper we elaborate on the structure of the Generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial…
This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for…
Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.
The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coefficients are allowed to depend on the whole trajectory of the…
This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking…
We develop a unified framework for constructing matrix approximations to the convolution operator of Volterra type defined by functions that are approximated using classical orthogonal polynomials on $[-1, 1]$. The numerically stable…
We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.
We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…
In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system…
A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
In this paper, we propose a hybrid collocation method based on finite difference and Haar wavelets to solve nonlocal hyperbolic partial differential equations. Developing an efficient and accurate numerical method to solve such problem is a…