Let $S_{\lambdab}$ be a bounded left-invertible weighted shift on a rootless directed tree T=(V,E). We address the question of when $S_{\lambdab}$ has Wold-type decomposition. We relate this problem to the convergence of ...

In this study, we developed the two-dimensional Legendre wavelet modified Petrov–Galerkin method for solving the two-dimensional moving boundary problem arising during melting of solid whose one surface is kept under most ...

This paper develops the hybridizable discontinuous Galerkin (HDG) method for a linear parabolic integro-differential equation and analyzes uniform in time error bounds. To handle the integral term, an extended Ritz-Volterra ...

This article develops and analyses a mixed virtual element scheme for the spatial discretization of linear parabolic integro-differential equations (PIDEs) combined with backward Euler’s temporal discretization approach. ...

In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is ...

This article presents and examines two distinctive approaches to the mixed virtual element method (VEM) applied to parabolic integro-differential equations (PIDEs) with non-smooth initial data. In the first part of the ...

In this article, a prion proliferation system in the presence of a chaperone, which involves two ODEs and an integro-partial differential equation, is studied. The existence of weak solution results obtained in Laurençot ...

This article presents analytic approximate solutions of the condensing coagulation model (CCM) and Lifshitz-Slyzov equation (LSE) using two different semi-analytical schemes, namely the homotopy perturbation and Adomian ...

The Oort–Hulst–Safronov equation is a relevant population balance model. Its discrete form, developed by Pavel Dubovski, is the main focus of our analysis. The existence and density conservation are established for ...

In this work, semi-analytical approaches such as the Adomian decomposition method (ADM), and variational iteration method (VIM) are examined to solve the aggregation, aggregation-breakage and pure growth equations in series ...