A stability result for a network of two triple junctions on the plane

Boutarfa, Bariza; Dassios, Ioannis

doi:10.1002/mma.3767

Cited by 10 publications

(7 citation statements)

References 13 publications

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“…However, under the initial conditions that we used, it can be easily proved that it holds. Theorem 2.1 can be used to further develop and study through FPDEs similar dynamical systems and networks; see previous studies 34-36 …”

Section: Resultsmentioning

confidence: 99%

Solution method for the time‐fractional hyperbolic heat equation

Dassios

Font

2020

Math Methods in App Sciences

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In this article, we propose a method to solve the time‐fractional hyperbolic heat equation. We first formulate a boundary value problem for the standard hyperbolic heat equation in a finite domain and provide an analytical solution by means of separation of variables and Fourier series. Then, we consider the same boundary value problem for the fractional hyperbolic heat equation. The fractional problem is solved using three different definitions of the fractional derivative: the Caputo fractional derivative and two recently defined alternative versions of this derivative, the Caputo–Fabrizio and the Atangana–Baleanu. A closed form of the solution is provided for each case. Finally, we compare the solutions of the fractional and the standard problem and show numerically that the solution of the standard hyperbolic heat equation can be retrieved from the solution of the fractional equation in the limit γ→2, where γ represents the exponent of the fractional derivative.

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Section: Resultsmentioning

confidence: 99%

Solution method for the time‐fractional hyperbolic heat equation

Dassios

Font

2020

Math Methods in App Sciences

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“…For example, it can be used into other macroeconomic models, or models where the memory effect appears, and models with delays, see (Dassios et al 2017;Moaaz et al 2020a, b). In addition, this updated form of Samuelson's model can provide new alternative methods to prove stability of similar dynamical systems, see (Apostolopoulos and Ortega 2018;Boutarfa and Dassios 2017;Dassios 2015bDassios , 2018a.…”

Section: Resultsmentioning

confidence: 99%

The Samuelson macroeconomic model as a singular linear matrix difference equation

Ortega

Barros

2020

Economic Structures

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Keynesian macroeconomics inspired the seminal work of (Samuelson 1939), who actually introduced the business cycle theory. Although primitive and using only the demand point of view, the Samuelson's prospect still provides an excellent insight into the problem and justification of business cycles appearing in national economies. In the past decades, many more sophisticated models have been proposed by other researchers, see

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“…In recent years, there has been a significant development in using matrix theory to study networks related to engineering problems [35][36][37][38] and the solutions of non-linear algebraic systems [39][40][41][42][43][44][45]. The idea is to provide new techniques and methods ready for software implementation in order to solve non-linear equations, similar to those for modelling gas pipelines.…”

Section: Literature Reviewmentioning

confidence: 99%

A Novel Approach to Model a Gas Network

et al. 2019

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The continuous uninterrupted supply of Natural Gas (NG) is crucial to today’s economy, with issues in key infrastructure, e.g., Baumgarten hub in Austria in 2017, highlighting the importance of the NG infrastructure for the supply of primary energy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent. Further complicating the management of the NG network is its role in supporting the electrical network. The fast response times of NG power plants and the potential to store energy in the network play a key role in adding flexibility across other energy systems. Traditionally, modelling the NG network relies on nonlinear pipe flow equations that incorporate the demand (load), flow rate, and physical network parameters including topography and NG properties. It is crucial that the simulations produce accurate results quickly. This paper seeks to provide a novel method to solve gas flow equations through a network under steady-state conditions. Firstly, the model is reformulated into non-linear matrix equations, then the equations separated into their linear and nonlinear components, and thirdly, the non-linear system is solved approximately by providing a linear system with similar solutions to the non-linear one. The non-linear equations of the NG transport system include the main variables and characteristics of a gas network, focusing on pressure drop in the gas network. Two simplified models, both of the Irish gas network (1. A gas network with 13 nodes, 2. A gas network with 109 nodes) are used as a case study for comparison of the solutions. Results are generated by using the novel method, and they are compared to the outputs of two numerical methods, the Newton–Raphson solution using MATLAB and SAINT, a commercial software that is used for the simulation of the gas network and electrical grids.

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A stability result for a network of two triple junctions on the plane

Cited by 10 publications

References 13 publications

Solution method for the time‐fractional hyperbolic heat equation

Solution method for the time‐fractional hyperbolic heat equation

The Samuelson macroeconomic model as a singular linear matrix difference equation

A Novel Approach to Model a Gas Network

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