An efficient parallel algorithm for the numerical solution for Singularly Perturbed Delay Differential Equations with Layer Behavior
DOI:
https://doi.org/10.29304/jqcm.2020.12.2.700Keywords:
Singularly perturbed boundary value problems, delay term, boundary layer, neural networkAbstract
The numerical solution of a Singularly Perturbed Delay Differential Equations (SPDDE) is defined as a very charged problematic of computational becouse to the non-local nature of this type of differential Equations. Prove that parallelism can be used to overawed these problems for this purpose we suggest the application of parallel processors as the best solution to overcome the difficulties of the perturbed that occurs in Perturbed Delay Differential Equations on a matching processer. Allowing to several latest publications, this process has been effectively applied to a big number of SPDDE rising from a change of application fields. The exact quality of the conception of parallelism is argued in fact and several examples are presented to demonstrate the feasibility of our approach.
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References
[1] Lange, C.G. and Miura, R.M. 1994,Singular perturbation analysis of boundary-value problems for differential-difference equations. v.small shifts with layer behavior, SIAM J. Appl. Math., 54, 249-272.
[ 2] Derstine, M.W., Gibbs, F.A.H.H.M.,and Kaplan, D.L. 1982, Bifurcation gap
in a hybrid optical system, Phys. Rev. A,26, 3720-3722.
[ 3] Glizer, V.Y. 2003, Asymptotic analysisand solution of a finite-horizon H1control problem for singularly-perturbed linear systems with small state delay, J. Optim. Theory Appl., 117, 295-325.
[4] Lange, C.G. and Miura, R.M. 1994,Singular perturbation analysis of boundary-value problems for differential-difference equations. vi.Small shifts with rapid oscillations, SIAM J. Appl. Math., 54, 273-283.
[ 5] Kadalbajoo, M.K. and Sharma, K.K. 2004, Numerical analysis of singularly perturbed delay differential equations with layer behavior, Applied Mathematics and Computation, 157,11-28.
[6] Kadalbajoo, M.K. and Sharma, K.K. 2008, A numerical method on finite difference for boundary value problems for singularly perturbed delay differential equations, Applied Mathematics and Computation, 197, 692-707.
[ 7] Gabil M. Amiraliyev and Erkan Cimen, 2010, Numerical method for a singularly perturbed convection–diffusion problem with delay, Applied Mathematics and Computation, 216, 2351-2359.
[ 8] Mohapatra, J. and Natesan, S. 2011, Uniformly convergent numerical method for singularly perturbed differential-difference equation using grid equidistribution, International Journal for Numerical Methods in Biomedical Engineering, 27, Issue 9, 1427-1445.
[9] Kadalbajoo, M. K. and Kumar, D. 2008, Fitted mesh B-spline collocation method for singularly perturbed differential–difference equations with small delay, Applied Mathematics and Computation, 204, 90-98.
[10] Tawfiq Luma N. M., Oraibi Yaseen A., (2013), "Fast Training Algorithms for Feed Forward Neural Networks", Ibn Al-Haitham Journal for Pure and Applied Science , NO. 1, Vol. 26:275-280.
[11] Gemechis File and Y. N. Reddy," Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift ",Department of Mathematics, National Institute of Technology, Warangal 506 004, India, International Journal of Differential Equations Volume 2012, Article ID 572723, 12 pages
[12] M.K.Kadalbajoo, K.K. Sharma, A numerical analysis of singularly perturbed de-lay differential equations with layer behavior, Appl. Math. Comput. 157(2004), 11-28.
[ 2] Derstine, M.W., Gibbs, F.A.H.H.M.,and Kaplan, D.L. 1982, Bifurcation gap
in a hybrid optical system, Phys. Rev. A,26, 3720-3722.
[ 3] Glizer, V.Y. 2003, Asymptotic analysisand solution of a finite-horizon H1control problem for singularly-perturbed linear systems with small state delay, J. Optim. Theory Appl., 117, 295-325.
[4] Lange, C.G. and Miura, R.M. 1994,Singular perturbation analysis of boundary-value problems for differential-difference equations. vi.Small shifts with rapid oscillations, SIAM J. Appl. Math., 54, 273-283.
[ 5] Kadalbajoo, M.K. and Sharma, K.K. 2004, Numerical analysis of singularly perturbed delay differential equations with layer behavior, Applied Mathematics and Computation, 157,11-28.
[6] Kadalbajoo, M.K. and Sharma, K.K. 2008, A numerical method on finite difference for boundary value problems for singularly perturbed delay differential equations, Applied Mathematics and Computation, 197, 692-707.
[ 7] Gabil M. Amiraliyev and Erkan Cimen, 2010, Numerical method for a singularly perturbed convection–diffusion problem with delay, Applied Mathematics and Computation, 216, 2351-2359.
[ 8] Mohapatra, J. and Natesan, S. 2011, Uniformly convergent numerical method for singularly perturbed differential-difference equation using grid equidistribution, International Journal for Numerical Methods in Biomedical Engineering, 27, Issue 9, 1427-1445.
[9] Kadalbajoo, M. K. and Kumar, D. 2008, Fitted mesh B-spline collocation method for singularly perturbed differential–difference equations with small delay, Applied Mathematics and Computation, 204, 90-98.
[10] Tawfiq Luma N. M., Oraibi Yaseen A., (2013), "Fast Training Algorithms for Feed Forward Neural Networks", Ibn Al-Haitham Journal for Pure and Applied Science , NO. 1, Vol. 26:275-280.
[11] Gemechis File and Y. N. Reddy," Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift ",Department of Mathematics, National Institute of Technology, Warangal 506 004, India, International Journal of Differential Equations Volume 2012, Article ID 572723, 12 pages
[12] M.K.Kadalbajoo, K.K. Sharma, A numerical analysis of singularly perturbed de-lay differential equations with layer behavior, Appl. Math. Comput. 157(2004), 11-28.
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Published
2020-07-18
How to Cite
Shwayyea, R. T. (2020). An efficient parallel algorithm for the numerical solution for Singularly Perturbed Delay Differential Equations with Layer Behavior. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(2), Math Page 97– 106. https://doi.org/10.29304/jqcm.2020.12.2.700
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Math Articles
