Exponential spline method for singularly perturbed third-order boundary value problems

• Autorzy: Wakjira Yohannis Alemayehu , Duressa Gemechis File

Identyfikatory

DOI

10.1515/dema-2020-0024

• Języki publikacji: EN

Abstrakty

EN

The exponential spline function is presented to find the numerical solution of third-order singularly perturbed boundary value problems. Convergence analysis of the method is briefly discussed, and it is shown to be sixth order convergence. To validate the applicability of the method, some model problems are solved for different values of the perturbation parameter, and the numerical results are presented both in tables and graphs. Furthermore, the present method gives more accurate solution than some methods existing in the literature.

Słowa kluczowe

EN

exponential spline; singular perturbation; boundary layers; convergence

PL

zaburzenia osobliwe; warstwa graniczna; konwergencja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 360--372
• Opis fizyczny: Bibliogr. 19 poz., rys., tab.

Twórcy

autor

Wakjira Yohannis Alemayehu

• Department of Mathematics, Dambi Dollo University, Dambi Dollo, P. O. Box 260, Ethiopia

autor

Duressa Gemechis File

• Department of Mathematics, Jimma University, Jimma, P. O. Box 378, Ethiopia

Bibliografia

• [1] Ghazala Akram and Imran Talib, Quartic non-polynomial spline solution of a third order singularly perturbed boundary value problem, Res. J. App. Sci. Eng. Technol. 7(2014), no. 23, 4859-4863, DOI: http://dx.doi.org/10.19026/rjaset.7.875.
• [2] Aynalem Tafere Chekole, Gemechis File Duresssa and Gashu Gadisa Kiltu, Non-polynomial septic spline method for singularly perturbed two point boundary value problems of order three, J. Taibah Univ. Sci. 13(2019), no. 1, 651-660, DOI: https://doi.org/10.1080/16583655.2019.1617986.
• [3] Ghulam Mustafa and Syeda Tehmina Ejaz, A subdivision collocation method for solving two point boundary value problems of order three, J. Appl. Anal. Comput. 7(2017), no. 3, 942-956, DOI: https://doi.org/10.11948/2017059.
• [4] Yohannis Alemayehu Wakjira, Gemechis File Duressa and Tesfaye Aga Bullo, Quintic non-polynomial spline method for third order singularly perturbed boundary value problems, J. King Saud Univ. Sci. 30(2018), no. 1, 131-137, DOI: https://doi.org/10.1016/j.jksus.2017.01.008.
• [5] Arshad Khan and Pooja Khandelwal, Numerical solution of third order singularly perturbed boundary value problems using exponential quartic spline, Thai J. Math. 17(2019), no. 3, 663-672.
• [6] Sonali Saini and Hradyesh Kumar Mishra, A new quartic b-spline method for third-order self-ad joint singularly perturbed boundary value problems, App. Math. Sciences 9(2015), no. 8, 399-408, DOI: http://dx.doi.org/10.12988/ams.2015.48654.
• [7] T. Valanarasu and N. Ramanujam, Asymptotic numerical method for singularly perturbed third order ordinary differential equations with a discontinuous source term, Novi Sad J. Math. 37(2007), no. 2, 41-57.
• [8] Ghazala Akram, Quartic spline solution of a third order singularly perturbed boundary value problem, ANZIAM J. 53(2011), no. E, E44-E58, DOI: https://doi.org/10.21914/anziamj.v53i0.4526.
• [9] Wei-Hua Luo, Ting-Zhu Huang, Guo-Cheng Wu, and Xian-Ming Gu, Quadratic spline collocation method for the time fractional subdiffusion equation, Appl. Math. Comput. 276(2016), 252-265, DOI: https://doi.org/10.1016/j.amc.2015.12.020.
• [10] Wei-Hua Luo, Ting-Zhu Huang, Liang Li, Hou-Biao Li, and Xian-Ming Gu, Quadratic spline collocation method and efficient preconditioner for the Helmholtz equation with the Sommerfeld boundary conditions, Japan J. Indust. Appl. Math. 33(2016), 701-720, DOI: https://doi.org/10.1007/s13160-016-0225-9.
• [11] Edward P. Doolan, John J. H. Miller, and Willy H. A. Schilders, Boundary Value Technique For Finding Numerical Solution to Boundary Value Problems for Third Order Singularly Perturbed Ordinary Differential Equations, Boole Press, 1980.
• [12] Pankaj Kumar Srivastava and Manoj Kumar, Numerical algorithm based on quintic non-polynomial spline for solving third-order boundary value problems associated with draining and coating flows, Chin. Ann. Math. Ser. B 33(2012), 831-840, DOI: https://doi.org/10.1007/s11401-012-0749-5.
• [13] Ghazala Akram and Afia Naheed, Solution of fourth order singularly perturbed boundary value problem using septic spline, Middle-East J. Sci. Res. 15(2013), no. 2, 302-311, DOI: https://doi.org/10.5829/idosi.mejsr.2013.15.2.789.
• [14] Reza Jalilian and Hamed Jaliliany, An O(h10) Methods for numerical solutions of some differential equations occurring in plate detection theory, IJMES 3(2015), no. 2. Available: https://vixra.org/pdf/1601.0339v1.pdf.
• [15] Riaz A. Usmani, Discrete variable methods for a boundary value problem with engineering applications, Math. Comp. 32(1978), no. 144, 1087-1096, DOI: https://doi.org/10.1090/S0025-5718-1978-0483496-5.
• [16] Eisa A. Al-Said, Numerical solution of third order boundary value problems, Int. J. Comput. Math. 78(2001), no. 1, 111-121, DOI: https://doi.org/10.1080/00207160108805100.
• [17] Eisa A. Al-Said and Muhammad Aslam Noor, Numerical solution of third-order systems of boundary value problems, Appl. Math. Comput. 190(2007), 332-338, DOI: https://doi.org/10.1016/j.amc.2007.01.031.
• [18] F. A. Abd El-Salam, A. A. El-Sabbagh and Z. A. Zaki, The Numerical solution of linear third-order boundary value problems using nonpolynomial spline technique, J. Am. Sci., 6(2010), no. 12, 303-309.
• [19] Bushra A. Taha and Ahmed R. Khlefha, Numerical Solution of third order BVPs by using non-polynomial spline with FDM, Nonlinear Anal. Differ. Equations, Hikari Ltd. 3(2015), no. 1, 1-21, DOI: http://dx.doi.org/10.12988/nade.2015.4817.