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Khan, Shahna, Khan, Arshad. (1402). Non-polynomial cubic spline method for solution of higher order boundary value problems. سامانه مدیریت نشریات علمی, 11(2), 225-240. doi: 10.22034/cmde.2022.49827.2072
Shahna Khan; Arshad Khan. "Non-polynomial cubic spline method for solution of higher order boundary value problems". سامانه مدیریت نشریات علمی, 11, 2, 1402, 225-240. doi: 10.22034/cmde.2022.49827.2072
Khan, Shahna, Khan, Arshad. (1402). 'Non-polynomial cubic spline method for solution of higher order boundary value problems', سامانه مدیریت نشریات علمی, 11(2), pp. 225-240. doi: 10.22034/cmde.2022.49827.2072
Khan, Shahna, Khan, Arshad. Non-polynomial cubic spline method for solution of higher order boundary value problems. سامانه مدیریت نشریات علمی, 1402; 11(2): 225-240. doi: 10.22034/cmde.2022.49827.2072

Non-polynomial cubic spline method for solution of higher order boundary value problems

Computational Methods for Differential Equations
مقاله 2، دوره 11، شماره 2، تیر 2023، صفحه 225-240    اصل مقاله (352.85 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.49827.2072
نویسندگان
Shahna Khan* 1؛ Arshad Khan2
1Department of Mathematics, Sri Venkateswara College, University of Delhi, New Delhi-21, India.
2Department of Mathematics, Jamia Millia Islamia, New Delhi-25, India.
چکیده
In this paper, a new algorithm based on non-polynomial spline is developed for the solution of higher order boundary value problems(BVPs). Employment of the method is done by decomposing the higher order BVP into a system of third order BVPs. Convergence analysis of the developed method is also discussed. The method is tested on higher order linear as well as non-linear BVPs which shows the accuracy and efficiency of the method and also compared our results with some existing fourth order methods.
کلیدواژه‌ها
Non-polynomial spline؛ Higher-order؛ Non-linear؛ Convergence analysis؛ Boundary value problems
مراجع
  • [1] R. P. Agarwal, Boundary Value Problems for Higher-Order Differential Equations, World Scientific Singapore, (1986).
  • [2] E. A. Al-Said and M. A. Noor, Cubic splines method for a system of third-order boundary value problems, Appl Math and Comput, 142(2003), 195–204.
  • [3] K. Farajeyan, J. Rashidinia, R. Jalilian, and N. R. Maleki, Application of spline to approximate the solution of singularly perturbed boundary-value problems, Computational Methods for Differential Equations, 8 (2020), 373–388.
  • [4] S. U. Islam, I. A. Tirmizi, F. Haq, and M. A. Khan, Non-polynomial splines approach to the solution of sixth-order boundary-value problems, Appl Math and Comput, 195 (2008), 270–284.
  • [5] S. U. Islam, I. A. Tirmizi, and M. A. Khan, Quartic non-polynomial spline approach to the solution of a system of third-order boundary-value problems, J Math Anal Appl 335 (2007), 1095–1104.
  • [6] N. Jha, R. K. Mohanty, and V. Chauhan, The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems, Intern J Comput Math, (2014), Article ID 527924, 12 pages.
  • [7] K. N. S. Kasi Viswanadham and S. M. Reddy, Numerical Solution of Ninth Order Boundary Value Problems by Petrov-Galerkin Method with Quintic B-splines as Basis Functions and Septic B-splines as Weight Functions, International Conference on Computational Heat and Mass Transfer-2015 Procedia Engineering, 127 (2015), 1227–1234.
  • [8] A. Khan and T. Aziz, The numerical solution of third-order boundary-value problems using quintic splines, Appl Math Comput, 137 (2003), 253–260.
  • [9] A. Khan and P. Khandelwal, Solution of Non-linear Sixth-order Two Point Boundary-value Problems Using Parametric Septic Splines, Intern J Nonlin Science, 12 (2011), 184–195.
  • [10] K. Maleknejad, J. Rashidinia, and H. Jalilian, Quintic Spline functions and Fredholm integral equation, Computational Methods for Differential Equations, 9 (2021), 211–224.
  • [11] M. Kumar and P. K. Srivastava, Computational Techniques for Solving Differential Equations by Cubic, Quintic, and Sextic Spline, Intern J Comput Methods in Engg Science and Mechanics, 10 (2009), 108–115.
  • [12] J. Rashidinia, M. Khazaei, and H. Nikmarvani, Spline collocation method for solution of higher order linear boundary value problems, J Pure Appl Math, 6 (2015), 38–47.
  • [13] S. M. Reddy, Collocation Method for Ninth Order Boundary Value Problems by Using Sextic B-splines, Intern Research Journal of Engg and Tech 3 (2016), 56–72.
  • [14] S. S. Siddiqi and G. Akram, Solutions of 12th order boundary value problems using non-polynomial spline tech- nique, Appl Math and Comput, 199 (2008), 559–571.
  • [15] S. S. Siddiqi and E. H. Twizell, Spline solutions of linear twelfth-order boundary value problems, Appl Math and Comput, 78 (1997), 371–390.
  • [16] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall Englewood Cliffs NJ, (1962).
  • [17] A. M. Wazwaz, Approximate solutions to boundary value problems of higher order by the modified decomposition method, Comput Math Appl, 40 (2000), 679–691.
  • [18] H. Zadvan and J. Rashidina, Development of non polynomial spline and New B-spline with application to solution of Klein-Gordon equation, Computational Methods for Differential Equations, 8 (2020), 794–814.
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