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. ...

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 ...

The Smoluchowski’s aggregation equation has applications in the field of bio-pharmaceuticals (Zidar et al., 2018 [1]), financial sector (Pushkin et al., 2004 [2]), aerosol science (Shen et al., 2020 [3]) and many others. ...

The varied applications of the aggregation and breakage equations in several fields of science have attracted many researchers to explore accurate novel methods to calculate their solutions. Due to the complexity of these ...

The work of this paper is motivated by the recently published article (Zeidan et al., Math Methods Appl Sci 43(5):2171–2188, 2020) in which the authors have discussed the Adomian decomposition method (ADM) to solve one ...