دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات44
تعداد شماره‌ها1,303
تعداد مقالات16,020
تعداد مشاهده مقاله52,486,281
تعداد دریافت فایل اصل مقاله15,213,461
AliPanah, Amjad, Mohammadi, Kaivan, Ghasemi, Mohammad. (1402). Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method. سامانه مدیریت نشریات علمی, 11(3), 643-663. doi: 10.22034/cmde.2022.52725.2218
Amjad AliPanah; Kaivan Mohammadi; Mohammad Ghasemi. "Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method". سامانه مدیریت نشریات علمی, 11, 3, 1402, 643-663. doi: 10.22034/cmde.2022.52725.2218
AliPanah, Amjad, Mohammadi, Kaivan, Ghasemi, Mohammad. (1402). 'Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method', سامانه مدیریت نشریات علمی, 11(3), pp. 643-663. doi: 10.22034/cmde.2022.52725.2218
AliPanah, Amjad, Mohammadi, Kaivan, Ghasemi, Mohammad. Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method. سامانه مدیریت نشریات علمی, 1402; 11(3): 643-663. doi: 10.22034/cmde.2022.52725.2218

Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method

Computational Methods for Differential Equations
مقاله 15، دوره 11، شماره 3، شهریور 2023، صفحه 643-663    اصل مقاله (198.51 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.52725.2218
نویسندگان
Amjad AliPanah* ؛ Kaivan Mohammadi؛ Mohammad Ghasemi
Department of Applied Mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Kurdistan, Iran.
چکیده
In this work, a non-classical sinc-collocation method is used to  find numerical solution of third-order boundary value problems. The novelty of this approach is based on using the weight functions in the traditional sinc- expansion. The properties of sinc-collocation are used to reduce the boundary value problems to a nonlinear system of algebraic equations which can be solved numerically. In addition, the convergence of the proposed method is discussed by preparing the theorems which show exponential convergence and guarantee its applicability. Several examples are solved and the numerical results show the efficiency and applicability of the method.
کلیدواژه‌ها
Non-classical؛ Sinc collocation method؛ Third-order؛ Boundary value problem؛ Convergence
مراجع
  • [1] A. Alipanah, M. Razzaghi, and M. Dehghan, Nonclassical pseudospectral method for the solution of brachistochrone problem, Chao. Solit. Fract., 34 (2007), 1622-1628.
  • [2] E. Babolian, A. Eftekhari, and A. Saadatmandi, A sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems, Comput. Appl. Math., 34 (2015), 45-63.
  • [3] B. Bialecki, Sinc-collocation methods for two-point boundary value problems, IMA J. Numer. Anal., 11 (1991), 357-375.
  • [4] H. N. Caglar, S. H. Caglar, E. H. Twizell, The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions, Int. J. Comput. Math., 71 (1999), 373-381.
  • [5] A. Eftekhari and A. Saadatmandi, DE-sinc-collocation method for solving a class of second-order nonlinear BVPs, Math. Interdisc. Res., 6 (2021), 11-22.
  • [6] T. S. EL-Danaf, Quartic nonpolynomial spline solutions for Third order two-point boundary value problem, Word Academy Sci. Eng. Techno., 45 (2008), 453-456.
  • [7] M. K. Eqbal, M. Abbas, and B. Zafar, New quartic B-spline approximation for numerical solution of third order singular boundary value problems, J. Math., 51 (2019), 43-59.
  • [8] F. i. Haq, I. Hussain, and A. Ali,  A Haar wavelets based  numerical method for third-order boundary and initial     value problems, World Applied Sciences Journal., 13 (2011), 2244-2251.
  • [9] Y. Q. Hasan and L. M. Zhu, A note on the use of modified adomian decomposition method for solving  singular  boundary value problems of higher-order ordinary differential equations, Commun. Nonlinear Sci Numer. Simul.,     14 (2009)m 3261-3265.
  • [10] S. U. Islam and I. Tirmizi, A smooth approximation for the  solution  of  special  non-linear third-order boundary-  value problems based on non-polynomial splines, Inter. J. Comput. Math., 83 (2006), 397-407.
  • [11] S. Khan and A. Khan, Non-polynomial cubic spline method for solution of higher order boundary value problems, Comput. Methods Differ. Equ., 11(2) (2023), 225-240.
  • [12] A. Khan and P. Khandelval, Numerical solution of third order sigularly perturbed boundary value problems using exponential quartic spline, Thai. J. Math., 17 (2019), 663-672.
  • [13] A. Khan and T. Aziz, The numerical solution of third-order boundary-value problems using quintic splines, Appl. Math. Comput., 137 (2003), 253-260.
  • [14] Z. Li, Y. Wang, and F. Tan, The solution of a class of third-order boundary value problems by the reproducing  kernel method, Abstr. Appl. Anal., (2012), 11 pages.
  • [15] J. Lin,  Y. Zuhui,  and C-S. Liu,  Solving nonlinear third-order three-point  boundary value problems by boundary  shape functions methods, Advan. Differ. Equ., 146 (2021), (2021).
  • [16] J. Lund and K. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM Philadelphia, 1992.
  • [17] H. K. Mishra and S. Saini, Quartic B-spline method for numerical solving singularly perturbed third-order boundary value problems, Amer. J. Numer. Anal., 3 (2015), 18-24.
  • [18] A. C. Morlet, Convergence of the sinc method for a fourth-order ordinary differential equation with an application, SIAM J. Numer. Anal., 32 (1995), 1475-1503.
  • [19] P. K. Pandey, A numerical method for the solution of general third order boundary value problem in ordinary differential equations, Bull. Inter. Math. Virt. Instit., 7 (2017), 129-138.
  • [20] P. K. Pandey, A finite difference method for the numerical solving general third order  boundary-value problem  with an internal boundary, ISSN 1066-369X, Russian. Math., 61 (2017), 29-38.
  • [21] A. Saadatmandi, A. Khani, and MR. Azizi, Numerical calculation of fractional  derivatives  for  the  sinc  functions  via Legendre polynomials, Math. Interdisc. Res., 5 (2020), 71-86.
  • [22] A. Saadatmandi and M. Razzaghi, The numerical solution of third-order boundary value problems using sinc- collocation method, Commun. Numer. Methods Eng., 23 (2007), 681-689.
  • [23] S. Saini and H. K. Mishra, A new quartic B-spline method for third-order sigularly perturbed boundary value problems, Appl. Math. Sci., 9 (2015), 399-408.
  • [24] B. Shizgal, A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related prob- lems, J. Comput. phys., 41 (1981), 309-328.
  • [25] F. Stenger, Approximations via whittakers cardinal function, J. Approx. Theory., 17 (1976), 222-240.
  • [26] F. Stenger, A sinc-Galerkin method of solution of boundary value problems, Math. Comput., 33 (1979), 85-109.
  • [27] F. Stenger, Numerical Methods based on Sinc and Analytic Functions, New York: Springer-Verlag, 1993.
  • [28] S. Taherkhani, I. Najafi, and B. Ghayebi, A pseudospectral sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and Sine-Gordon equations, Comput. Methods Differ. Equ., 11(2) (2023), 357-368.
  • [29] Y. A. Wakjira and G. F. Duressa, Exponential spline method for singularly perturbed third-order boundary value problems, Demon. Math., 53 (2020), 360-372.
  • [30] Y. H. Youssri, S. M. Sayed, A. S. Mohamed, E. M. Aboeldahab, and W. M. Abd-Elhameed, Modified lucas polynomials for the numerical treatment of second-order boundary value problems,  Comput. Methods Differ. Equ, 11(1) (2023), 12-31 .
آمار
تعداد مشاهده مقاله: 407
تعداد دریافت فایل اصل مقاله: 500


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب