Growth of solutions for a coupled nonlinear Klein–Gordon system with strong damping, source, and distributed delay terms

Rahmoune, Abdelaziz; Ouchenane, Djamel; Boulaaras, Salah; Agarwal, Praveen

doi:10.1186/s13662-020-02801-y

Cited by 22 publications

(9 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Future work includes studying the new algorithm on nonlinear least squares problems as discussed in [ 40 ]. Furthermore, we shall consider other problems in our future research as presented in the following references [ 41 – 44 ].…”

Section: Discussionmentioning

confidence: 99%

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

et al. 2022

View full text Add to dashboard Cite

The three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.

show abstract

Section: Discussionmentioning

confidence: 99%

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

et al. 2022

View full text Add to dashboard Cite

show abstract

“…For some other applications in the related area, we refer readers to previous works. [20][21][22][23][24][25] Motivated from the real case and overconvergence properties of above work on complex operators, we consider the complex form of the operators (1.2), for n ∈ N, 𝛼 ∈ [0, 1], z ∈ C and 𝑓 ∶ [0, 1] → C, a complex valued analytic function as follows:…”

Section: Introductionmentioning

confidence: 99%

Approximation properties of complex genuine α–Bernstein‐Durrmeyer operators

Goyal

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

Herein, we propose a complex form of genuine Bernstein‐Durrmeyer type operators depending on a non‐negative real parameter α$$ \alpha $$. We present the quantitative upper bound, Voronovskaja type result and the exact order of approximation for the derivatives of the operators attached to analytic functions on compact disks. These results validate the extension of approximation properties of complex genuine α$$ \alpha $$–Bernstein‐Durrmeyer type operators from real intervals to compact disks in the complex plane.

show abstract

“…e functional differential equation has been multiplied by small parameter (0 < ε < 1) in the highest order derivative term called the singularly perturbed mixed delay differential equations. e main determination for such a problem is the study of biological science, epidemics, and population [5][6][7][8][9][10]. e authors in [11] have considered functional differential equation in singularly perturbed problems, such as…”

Section: Introductionmentioning

confidence: 99%

Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

Hammachukiattikul

Sekar

Tamilselvan

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20).

show abstract

Growth of solutions for a coupled nonlinear Klein–Gordon system with strong damping, source, and distributed delay terms

Abstract: In this work, the exponential growth of solutions for a coupled nonlinear Klein–Gordon system with distributed delay, strong damping, and source terms is proved. Take into consideration some suitable assumptions.

Cited by 22 publications

References 27 publications

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

Approximation properties of complex genuine α–Bernstein‐Durrmeyer operators

Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

Contact Info

Product

Resources

About