Higher-order multi-step Runge-Kutta-Nystr\

Jasim, Athraa Abdulsalam; Senu, Norazak; Abdul Majid, Zanariah; Nik Long, Nik Mohd Asri

doi:10.22034/cmde.2024.57684.2418

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	44
تعداد شماره‌ها	1,303
تعداد مقالات	16,020
تعداد مشاهده مقاله	52,489,394
تعداد دریافت فایل اصل مقاله	15,216,948

	Higher-order multi-step Runge-Kutta-Nystr\"om methods with frequency-dependent coefficients for second-order initial value problem $u^{\prime \prime}=f(x,u,u^{\prime})$
Computational Methods for Differential Equations
مقاله 13، دوره 12، شماره 4، دی 2024، صفحه 808-826 اصل مقاله (647.78 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57684.2418
نویسندگان
Athraa Abdulsalam Jasim¹؛ Norazak Senu^* ²؛ Zanariah Abdul Majid²؛ Nik Mohd Asri Nik Long²
¹1- Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq.\\ 2- Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
²1- Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.\\ 2- Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
چکیده
In this study, for the numerical solution of general second-order ordinary differential equations (ODEs) that exhibit oscillatory or periodic behavior, fifth- and sixth-order explicit multi-step Runge-Kutta-Nystr¨om (MSGRKN) methods, respectively, are constructed. The parameters of the proposed methods rely on the frequency ω of each problem whose solution is a linear combination of functions {e(iωx), e(−iωx)} or {cos(ωx), sin(ωx)}. The study also includes an analysis of the linear stability of the suggested methods. The numerical results indicate the efficiency of the proposed methods in solving such problems compared to methods with similar characteristics in the literature.
کلیدواژه‌ها
Explicit methods؛ Trigonometrical fitting؛ Multi-step Runge-Kutta-Nystr\"om methods؛ Initial value problems؛ General second-order oscillatory differential equations

مراجع
[1] S. Abbas, N. A. Arifi, M. Benchohra, J. Henderson, Coupled Hilfer and Hadamard random fractional differential systems with finite delay in generalized Banach spaces, Differ. Equ. Appl., 12 (2020), 337–353. [2] B. Ahmad, A. Alsaedi, S. K. Ntouyas, and J. Tariboon, Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Springer, Cham, 2017. [3] G. Alotta, E. Bologna, G. Failla, and M. Zingales, A Fractional Approach to Non-Newtonian Blood Rheology in Capillary Vessels, J. Peridyn Nonlocal Model, 1 (2019), 88–96. [4] M. Benchohra, F. Berhoun, S. Hamani, J. Henderson, S. K. Ntouyas, A. Ouahab, and I. K. Purnaras, Eigenvalues for iterative systems of nonlinear boundary value problems on time scales, Nonlinear Dyn. Syst. Theory, 9(1) (2009), 11–22. [5] P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl., 269 (2002), 1–27. [6] P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl., 270 (2002), 1–15. [7] K. Demling, Nonlinear Functional Analysis, Springer, New York, 1985. [8] Y. Ding, J. Jiang, D. O’Regan, and J. Xu, Positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities, Complexity, 2020 (2020), Article ID 9742418, 1–14. [9] E. Egri, A boundary value problem for a system of iterative functional-differential equations, Carpathian J. Math., 24(1) (2008), 23–36. [10] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, 1988. [11] E. F. D. Goufo, A biomathematical view on the fractional dynamics of cellulose degradation, Fract. Calc. Appl. Anal., 18(3) (2015), 554–564. [12] J. Hadamard, Essai sur letude des fonctions donnes par leur developpement de Taylor, J. Mat. Pure et Appl., Sr. 4, 8 (1892), 101–186. [13] M. Khuddush, Existence of solutions to the iterative system of nonlinear two-point tempered fractional order boundary value problems, Adv. Studies: Euro-Tbilisi Math. J., 16(2) (2023), 97–114. [14] A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc., 38 (2001), 1191–1204. [15] A. A. Kilbas and J. J. Trujillo, Hadamard-type integrals as G-transforms, Integral Transforms Spec. Funct., 14 (2003), 413–427. [16] A. A. Kilbas, H. M. Srivasthava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier, Amsterdam, 204 (2006). [17] A. N. Kochubei, Y. F. Luchko, V. E. Tarasov, and I. Petras, Handbook of fractional calculus with applications, Applications in Physics part A., De Gruyter, 2019. [18] A. N. Kochubei, Y. F. Luchko, V. E. Tarasov, and I. Petras, Handbook of fractional calculus with applications, Applications in Physics part B., De Gruyter, 2019. [19] M. A. Krasnosel’skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964. [20] B. M. B. Krushna, Eigenvalues for iterative systems of Riemann–Liouville type p-Laplacian fractional-order boundary-value problems in Banach spaces, Comput. Appl. Math., 39 (2020), 1–15. [21] R. Y. Ma, Multiple nonnegative solutions of second order systems of boundary value problems, Nonlin. Anal. 42 (2000), 1003–1010. [22] M. M. Matar, J. Alzabut, and J. J. Mohan, A coupled system of nonlinear Caputo-Hadamard Langevin equations associated with nonperiodic boundary conditions, Math. Methods Appl. Sci., 44 (2021), 2650–2670. [23] I. Podulbny, Fractional Differential Equations, Academic Press, San Diego, 1999. [24] K. R. Prasad and B. M. B. Krushna, Solvability of p-Laplacian fractional higher order two-point boundary value problems, Commun. Appl. Anal., 19 (2015), 659–678. [25] K. R. Prasad, B. M. B. Krushna, V. V. R. R. B. Raju, and Y. Narasimhulu, Existence of positive solutions for systems of fractional order boundary value problems with Riemann–Liouville derivative, Nonlinear Stud., 24 (2017), 619–629. [26] K. R. Prasad, B. M. B. Krushna, and N. Sreedhar, Even number of positive solutions for the system of (p,q)Laplacian fractional order two-point boundary value problems, Differ. Equ. Dyn. Syst., 26 (2018), 315–330. [27] K. R. Prasad, B. M. B. Krushna and L. T. Wesen, Existence results for positive solutions to iterative systems of four-point fractional-order boundary value problems in a Banach space, Asian-Eur. J. Math., 13 (2020), 1–17. [28] M. Seghier, A. Ouahab, and J. Henderson, Random solutions to a system of fractional differential equations via the Hadamard fractional derivative, Eur. Phys. J. Spec. Top., 226 (2017), 3525–3549. [29] H. H. Sherief and M. A. el-Hagary, Fractional order theory of thermo-viscoelasticity and application, Mech TimeDepend Mater., 24 (2020), 179–195. [30] H. Sun, W. Chen, C. Li, and Y.Q. Chen, Fractional differential models for anomalous diffusion, Physica A: Statistical mechanics and its applications, 389 (2010), 2719–2724. [31] H. G. Sun, Y. Zhang, D. Baleanu, W. Chen, and Y. Q. Chen, A new collection of real world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci. Numer. Simul., 64 (2018), 213–231. [32] P. Thiramanus, S. K. Ntouyas, and J. Tariboon, Positive solutions for Hadamard fractional differential equations on infinite domain, Adv. Difference Equ., 2016 (2016), 1–18. [33] K. Pei, G. T. Wang, and Y. Y. Sun, Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain, Appl. Math. Comput., 312 (2017), 158–168. [34] J. Tariboon, S. K. Ntouyas, S. Asawasamrit, and C. Promsakon, Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain, Open Math., 15 (2017), 645–666. [35] G. T. Wang, K. Pei, R. P. Agarwal, L. H. Zhang, and B. Ahmad, Nonlocal Hadamard fractional boundary value problem with Hadamard integral and discrete boundary conditions on a half-line, J. Comput. Appl. Math., 343 (2018), 230–239. [36] W. Yang, Positive solutions for singular Hadamard fractional differential system with four-point coupled boundary conditions, J. Appl. Math. Comput., 49 (2015), 357–381. [37] C. Zhai, W. Wang, and H. Li, A uniqueness method to a new Hadamard fractional differential system with four-point boundary conditions, J Inequal Appl 2018, 207 (2018). [38] W. Zhang and W.B. Liu, Existence, uniqueness, and multiplicity results on positive solutions for a class of Hadamard-type fractional boundary value problem on an infinite interval, Math. Methods Appl. Sci., 43 (2020), 2251–2275. [39] C. Zhai and W. Wang, Solutions for a system of Hadamard fractional differential equations with integral conditions, Numer. Funct. Anal. Optim., 41 (2020), 209–229. [40] W. Zhang and J. Ni, New multiple positive solutions for Hadamard-type fractional differential equations with nonlocal conditions on an infinite interval, Appl. Math. Lett., 118 (2021), 1–10.
آمار تعداد مشاهده مقاله: 197 تعداد دریافت فایل اصل مقاله: 370

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Higher-order multi-step Runge-Kutta-Nystr\"om methods with frequency-dependent coefficients for second-order initial value problem $u^{\prime \prime}=f(x,u,u^{\prime})$