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 ...

This article develops a new semi-analytical technique based on the homotopy analysis approach for solving linear or non-linear differential equations and the results are compared to the well-known approaches such as the ...

The dynamics of innumerable real-world phenomena is represented with the help of non-linear ordinary differential equations (NODEs). There is a growing trend of solving these equations using accurate and easy to implement ...

The accelerated homotopy perturbation Elzaki transform method (AHPETM), which is based on the homotopy perturbation method (HPM), is used in this article to solve the Burgers equation and system of Burgers equations. AHPETM ...

The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method ...