Cubic B-splines Method for Solving Singularly Perturbed Delay Partial Differential Equations
DOI:
https://doi.org/10.29304/jqcm.2021.13.3.821Keywords:
Delay parabolic partial differential equation singular perturbations, boundary layers, cubic B-spline, Taylor’s series expansion, exact solutionAbstract
In this paper, we use the cubic B-splines method to solve the singular perturbed delay partial differential equations where the propagation term is multiplied by a small perturbation coefficient. In general, solutions to this type of problem have a boundary layer. The accuracy of the method was tested with two numerical examples and the results were compared with exact solutions and other methods.
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References
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[7] N. A. Mbroh and J. B. Munyakazi, A fitted operator finite difference method of linesfor singularly perturbed parabolic convection{diffusion problems. Mathematics and Computers in Simulation, 165 (2019) 156-171.
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[10] J. Singh, S. Kumar, and M. Kumar, A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay. Numerical Methods for Partial Differential Equations, 34 (2018) 1849-1866.
[11] R. N. Rao and P. P. Chakravarthy, A fitted numerov method for singularly perturbed parabolic partial differential equation with a small negative shift arising in control theory. Numerical Mathematics: Theory, Methods and Applications, 7 (2014) 23-40.
[12] D.and Li Z. Wang, Y.and Tian, Numerical method for singularly perturbed delay parabolic partial differential equations. Thermal Science, 21(2017) 1595-1599.
[13] Al-Humedi, H., & jameel, Z, "Combining Cubic B-Spline Galerkin Method with Quadratic Weight Function for Solving Partial Integro-Differential Equations." ,Journal of Al-Qadisiyah for computer science and mathematics ,12 (2020) Page-9.
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[14] Shwayyea, R.,"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(2020) Page-97.
[15] Mindeel. M. Al-Abrahemee, K ,"Solving Singular Perturbed Boundary Value Problems By using Semi-Analytic Method.", Journal of AL-Qadisiyah for computer science and mathematics 8 (2016) 67-77.
[16] H. AL - Sharoot, M., & T. Khanjar, M ,"A comparison of some semi-parametric Estimators For Partial Linear Regression Model by using simulation." Journal of Al-Qadisiyah for computer science and mathematics 7 (2015) 42-29.
[17] younis kawi, H., & Salih Abdul-Razaq, T, "Single Machine Scheduling To Minimize a Function of Square Completion Time and Maximum Earliness Simultaneously.", Journal of Al-Qadisiyah for computer science and mathematics ,2 (2010) 79-95.
[2] E . B.M. Bashier and K. C, Patidar. A novel fitted operator finite difference methodfor a singularly perturbed delay parabolic partial differential equation. Applied mathematics and Computation, 217 (2011) 4728-4739.
[3] G. F. Gelu, F. W.and Duressa, A uniformly convergent collocation method for singularly perturbed delay parabolic reaction-diffusion problem. In Abstract and Applied Analysis, Vol. 2021. Hindawi, 2021.
[4] S. Gowrisankar and S. Natesan, A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problemsonequidistributed grids. Electron. Trans. Numer. Anal 41 (2014) 376-395.
[5] S. Gowrisankar and S. Natesan, "-uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations. International Journalof Computer Mathematics, 94 (2017) 902-921.
[6] S. Kumar and M. Kumar, High order parameter-uniform discretization for singularlyperturbed parabolic partial differential equations with time delay. Computers & Mathematics with Applications, 68 (2014) 1355-1367.
[7] N. A. Mbroh and J. B. Munyakazi, A fitted operator finite difference method of linesfor singularly perturbed parabolic convection{diffusion problems. Mathematics and Computers in Simulation, 165 (2019) 156-171.
[8] S. Khurana and M. Thachuk, Collocation methods for the boltzmann equation; hot atom relaxation and ion transport in gases. In AIP Conference Proceedings, Vol. 1333. No. 1. American Institute of Physics, 2011.
[9] B. Qiao, X. Chen, X. Xue, X. Luo, and R. Liu, The application of cubic b-spline collocation method in impact force identification. Mechanical Systems and Signal Processing, 64 (2015) 413-427.
[10] J. Singh, S. Kumar, and M. Kumar, A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay. Numerical Methods for Partial Differential Equations, 34 (2018) 1849-1866.
[11] R. N. Rao and P. P. Chakravarthy, A fitted numerov method for singularly perturbed parabolic partial differential equation with a small negative shift arising in control theory. Numerical Mathematics: Theory, Methods and Applications, 7 (2014) 23-40.
[12] D.and Li Z. Wang, Y.and Tian, Numerical method for singularly perturbed delay parabolic partial differential equations. Thermal Science, 21(2017) 1595-1599.
[13] Al-Humedi, H., & jameel, Z, "Combining Cubic B-Spline Galerkin Method with Quadratic Weight Function for Solving Partial Integro-Differential Equations." ,Journal of Al-Qadisiyah for computer science and mathematics ,12 (2020) Page-9.
.
[14] Shwayyea, R.,"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(2020) Page-97.
[15] Mindeel. M. Al-Abrahemee, K ,"Solving Singular Perturbed Boundary Value Problems By using Semi-Analytic Method.", Journal of AL-Qadisiyah for computer science and mathematics 8 (2016) 67-77.
[16] H. AL - Sharoot, M., & T. Khanjar, M ,"A comparison of some semi-parametric Estimators For Partial Linear Regression Model by using simulation." Journal of Al-Qadisiyah for computer science and mathematics 7 (2015) 42-29.
[17] younis kawi, H., & Salih Abdul-Razaq, T, "Single Machine Scheduling To Minimize a Function of Square Completion Time and Maximum Earliness Simultaneously.", Journal of Al-Qadisiyah for computer science and mathematics ,2 (2010) 79-95.
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Published
2021-07-25
How to Cite
Bloshi, Z. S., & Taha, B. A. (2021). Cubic B-splines Method for Solving Singularly Perturbed Delay Partial Differential Equations. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(3), Math Page 1– 12. https://doi.org/10.29304/jqcm.2021.13.3.821
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Math Articles
