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The general implicit-block method with two-points and extra derivatives for solving fifth-order ordinary differential equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 90، دوره 13، شماره 1، خرداد 2022، صفحه 1081-1097 اصل مقاله (535.58 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5650 | ||
| نویسندگان | ||
| Mohammed Yousif Turki1؛ Shaymaa Y. Alku* 2؛ Mohammed S. Mechee3 | ||
| 1Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Iraq | ||
| 2Department of Mathematics, College of Computer Science and Mathematics, University of Kufa, Najaf, Iraq | ||
| 3Information Technology Research and Development Center (ITRDC), University of Kufa, Najaf, Iraq | ||
| تاریخ دریافت: 25 فروردین 1400، تاریخ بازنگری: 12 مرداد 1400، تاریخ پذیرش: 03 شهریور 1400 | ||
| چکیده | ||
| In this work, a general implicit block method (GIBM) with two points for solving general fifth-order initial value problems (IVPs) has been derived. GIBM is proposed by adopting the basis functions of Hermite interpolating polynomials. GIBM is presented to be suitable with the numerical solutions of fifth-order IVPs. Hence, the derivation of GIBM has been introduced. Numerical implementations compared with the existing numerical GRKM method are used to prove the accuracy and efficiency of the proposed GIBM method. The impressive numerical results of the test problems using the proposed GIBM method agree well with the approximated solutions of them using the existing GRKM method. | ||
| کلیدواژه‌ها | ||
| Implicit numerical method؛ ODEs؛ IVPs؛ Block method؛ Order؛ RKM؛ GRKM؛ Fifth-order؛ Ordinary differential equations | ||
| مراجع | ||
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[1] E. Twizell and A. Boutayeb, Numerical methods for the solution of special and general sixth-order boundary-value problems, with applications to b´enard layer eigenvalue problems, Proc. R. Soc. Lond. A 431(1883) (1990) 433–450. [2] J. Toomre, J.-P. Zahn, J. Latour and E. Spiegel, Stellar convection theory, ii-singlemode study of the second convection zone in an a-type star, Astrophysical J. 207 (1976) 545–563. [3] A. Boutayeb and E. Twizell, Numerical methods for the solution of special sixth-order boundary-value problems, Int. J. Comput. Math. 45(3-4) (1992) 207–223. [4] E. Twizell, Numerical Methods for Sixth-order Boundary Value Problems, Numerical Mathematics Singapore, Springer, 1988. [5] G. Akram and S.S. Siddiqi, Solution of sixth order boundary value problems using nonpolynomial spline technique, Appl. Math. Comput. 181(1) (2006) 708–720. [6] M. S. Mechee and M. A. Kadhim, Explicit direct integrators of rk type for solving special fifth-order ordinary differential equations, Amer. J. Appl. Sci. 13 (2016) 1452–1460. [7] M. Mechee and M. Kadhim, Direct explicit integrators of rk type for solving special fourth-order ordinary differential equations with an application, Global J. Pure Appl. Math. 12(6) (2016) 4687–4715. [8] M.S. Mechee and J.K. Mshachal, Derivation of embedded explicit rk type methods for directly solving class of seventh-order ordinary differential equations, J. Interdisciplinary Math. 22(8) (2019) 1451–1456. [9] M. Mechee, F. Ismail, N. Senu and Z. Siri, Directly solving special second order delay differential equations using runge-kutta-nystrom method, Math. Prob. Engin. 2013 (2013). [10] M. Mechee, N. Senu, F. Ismail, B. Nikouravan and Z. Siri, A three-stage fifth-order runge-kutta method for directly solving special third-order differential equation with application to thin film flow problem, Math. Prob. Engin. 2013 (2013). [11] M. Mechee, F. Ismail, Z. Hussain and Z. Siri, Direct numerical methods for solving a class of third-order partial differential equations, Appl. Math. Comput. 247 (2014) 663–674. [12] M. Mechee, F. Ismail, Z. Siri, N. Senu and Senu, A four-stage sixth-order rkd method for directly solving special third order ordinary differential equations, Life Sci. J. 11(3) (2014). [13] M. Mechee, Direct integrators of runge-kutta type for special third-order differential equations with their applications, Thesis, ISM, University of Malaya, 2014. [14] M. Mechee, F. Ismail, N. Senu and Siri, A third-order direct integrators of runge-kutta type for special third-order ordinary and delay differential equations, J. Appl. Sci. 2(6) (2014). [15] M. Mechee, Z.M. Hussain, and H.R. Mohammed, On the reliability and stability of direct explicit runge-kutta integrators, Global J. Pure Appl. Math. 12(4) (2016) 3959–3975. [16] M.S. Mechee and Y. Rajihy, Generalized rk integrators for solving ordinary differential equations: A survey & comparison study, Global J. Pure Appl. Math. 13(7) (2017) 2923–2949. [17] M.S. Mechee, G.A. Al-Juaifri and A.K. Joohy, Modified homotopy perturbation method for solving generalized linear complex differential equations, Appl. Math. Sci. 11(51) (2017) 2527–2540. [18] M.S. Mechee and J.K. Mshachal, Derivation of direct explicit integrators of rk type for solving class of seventh-order ordinary differential equations, Karbala Int. J. Modern Sci. 5(3) (2019) 8. [19] M.S. Mechee, Generalized rk integrators for solving class of sixth-order ordinary differential equations, J. Interdisciplinary Math. 22(8) (2019) 1457–1461. [20] M.S. Mechee, O.I. Al-Shaher and G.A. Al-Juaifri, Haar wavelet technique for solving fractional differential equations with an application, J. Al-Qadisiyah Comput. Sci. Math. 11(1) (2019) 70. [21] M.S. Mechee, H.M. Wali and K.B. Mussa, Developed rkm method for solving ninth order ordinary differential equations with applications, J. Phys. Conf. Ser. 1664(1) (2020) 012102. [22] M.S. Mechee and K.B. Mussa, Generalization of rkm integrators for solving a class of eighth-order ordinary differential equations with applications, Adv. Math. Mod. Appl. 5(1) (2020) 111–120. [23] M.S. Mechee and N. Senu, A new numerical multistep method for solution of second order of ordinary differential equations, Asian Trans. Sci. Tech. 2(2) (2012) 18–22. [24] R. Allogmany, F. Ismail and Z.B. Ibrahim, Implicit two-point block method with third and fourth derivatives for solving general second order odes, Math. Stat. 7(4) (2019) 116–123. [25] R. Allogmany and F. Ismail, Direct solution of u” = f(t, u, u′) using three-point block method of order eight with applications, J. King Saud University Sci. 33(2) (2021) 101337. [26] R. Allogmany, F. Ismail, Z.A. Majid and Z.B. Ibrahim, Implicit two-point block method for solving fourth-order initial value problem directly with application, Math. Prob. Engin. 2020 (2020). [27] M.Y. Turki, F. Ismail, N. Senu and Z. Bibi, Two and three point implicit second derivative block methods for solving first order ordinary differential equations, ASM Sci. J. 12 (2019) 10–23. [28] M.Y. Turki, Second derivative block methods for solving first and higher order ordinary differential equations, PhD Thesis, UPM, Putra University, 2018. [29] M.Y. Turki, F. Ismail, N. Senu, and Z.B. Ibrahim, Second derivative multistep method for solving first-order ordinary differential equations, AIP Conf. Proc. 1739(1) (2016) 020054. [30] M. Turki, F. Ismail, N. Senu, and Z.B. Ibrahim, Direct integrator of block type methods with additional derivative for general third order initial value problems, Adv. Mech. Engin. 12(10) (2020) 1687814020966188. [31] M. S. Mechee and F. Fawzi, Generalized runge-kutta integrators for solving fifth-order ordinary differential equations, Italian J. Pure Appl. Math. 45 (2021) 600–610. [32] X. You and Z. Chen, Direct integrators of runge-kutta type for special third-order ordinary differential equations, Appl. Numerical Math. 74 (2013) 128–150. [33] K. Hussain, F. Ismail and N. Senu, Runge-kutta type methods for directly solving special fourth-order ordinary differential equations, Math. Prob. Engin. 2015 (2015). | ||
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