scholarly journals Numerical Approach for Differential-Difference Equations having Layer Behaviour with Small or Large Delay using Non-Polynomial Spline

2021 ◽  
Author(s):  
M Lalu ◽  
K. Phaneendra ◽  
Siva Prasad Emineni
Keyword(s):  
Difference Equations ◽  
Numerical Scheme ◽  
Numerical Approach ◽  
Polynomial Spline ◽  
Singular Perturbation Theory ◽  
Oscillatory Behaviour ◽  
Large Delay ◽  
First Order ◽  
Solution Layer ◽  
The Impact

Abstract A numerical approach is suggested for the layer behaviour differential-difference equations with small and large delays in the differentiated term. Using the non-polynomial spline, the numerical scheme is derived. The discretization equation is constructed using the first order derivative continuity at non-polynomial spline internal mesh points. A fitting parameter is introduced into the scheme with the help of the singular perturbation theory to minimize the error in the solution. The maximum errors in the solution are tabulated to verify the competence of the numerical method relative to the other methods in literature. We also focused on the impact of large delays on the layer behaviour or oscillatory behaviour of solutions using a special mesh with and without fitting parameter in the proposed scheme. Graphs show the effect of the fitting parameter on the solution layer.

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

2020 ◽  
Author(s):  
A. I. Lopato ◽  
◽  
A. G. Eremenko ◽  
Keyword(s):  
Chemical Kinetics ◽  
Numerical Scheme ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Numerical Approach ◽  
Detonation Waves ◽  
Detailed Chemical Kinetics ◽  
Parallel Solver ◽  
Further Development ◽  
Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

scholarly journals Influence of Age on the Technical Wear of Tenement Houses

2020 ◽  
Vol 11 (1) ◽  
pp. 297
Author(s):  
Jarosław Konior ◽  
Marek Sawicki ◽  
Mariusz Szóstak
Keyword(s):  
Residential Buildings ◽  
Residential Building ◽  
Numerical Approach ◽  
Technical Condition ◽  
Visual Methods ◽  
Secondary Importance ◽  
Building Maintenance ◽  
Technical Maintenance ◽  
Traditional Construction ◽  
The Impact

The research presented in the article, which includes methods, models, and conclusions, contains synthetic and analytical model solutions concerning the problems of the technical maintenance and wear of residential buildings with a traditional construction. The cause and effect relationships between the occurrence of damage in the elements of tenement houses (treated as proof of their maintenance conditions), and the size of the technical wear of these elements were determined using a representative and purposefully selected sample of 102 residential buildings erected during the second half of the nineteenth and early twentieth centuries in Wroclaw’s “Downtown” district. Quantitative damage analysis, which was carried out using empirical (visual) methods of assessing the technical condition of a building, indicates the type and size of damage to the building’s elements that are characteristic for the relevant maintenance conditions. Research concerning the cause–effect relationships (“damage–technical wear”) in observed states allows for a numerical approach to the impact of building maintenance conditions on the degree of the technical wear of its components. The maintenance and exploitation conditions determine the degree of the technical wear of the elements of an old residential building. The exploitation condition of these buildings is manifested by damage to elements caused by water and moisture penetration, which is especially important for poorly maintained buildings. The article shows that the age of the elements of an old residential building with a traditional construction is of secondary importance in the process of the intensity of losing its serviceability value. It was calculated that no more than 30% of the damage of building components is explained by the passage of time, and it is therefore not age that determines the course of the technical wear of the elements of the analyzed tenement houses.

scholarly journals Note on constructing a family of solvable sine-type difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Stevo Stević ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
First Order ◽  
Solvable In Closed Form

AbstractWe obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

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