The authors would like to inform the readers that the conditions of Theorem 2.2 and Theorem 3.1 of Yadav et al. (2024) is not adequate. The statement and proof of Theorems 2.2 and 3.1 of Yadav et al. (2024) have been ...

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary ...

We propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is ...

Backward Euler for two dimensional Sobolev equation is discussed in this article. We begin by obtaining some basic a priori estimates for the semi-discrete scheme and for the backward Euler approximation. It is proven that ...

This article presents and analyzes a mixed virtual element approach for discretizing parabolic integro-differential equations in a bounded subset of , in addition to the backward Euler approach for temporal discretization. ...

This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler’s scheme for temporal discretization. With the ...

The hybridizable discontinuous Galerkin (HDG) method has been applied to a nonlinear parabolic integro-differential equation. The nonlinear functions are considered to be Lipschitz continuous to analyze uniform in time a ...

This article is dedicated to analyze a finite volume scheme for solving coagulation and multiple fragmentation equation. The rates of coagulation and fragmentation are chosen locally bounded and unbounded (singularity near ...

In the present work, a mathematical model which consists of a nonlinear partial integro-differential equation coupled with two ordinary differential equations (ODEs) is analyzed. This model describes the relation between ...

The objectives of this article are to deal with computing the series solutions of 1D dimensionless Burgers’ equation using the optimized decomposition method (ODM) and the extension of ODM to the system of PDEs which aids ...