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Thirumalai, Sagithya, Seshadri, Rajeswari, Yuzbasi, Suayip. (1402). Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations. سامانه مدیریت نشریات علمی, 11(3), 589-604. doi: 10.22034/cmde.2022.51962.2170
Sagithya Thirumalai; Rajeswari Seshadri; Suayip Yuzbasi. "Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations". سامانه مدیریت نشریات علمی, 11, 3, 1402, 589-604. doi: 10.22034/cmde.2022.51962.2170
Thirumalai, Sagithya, Seshadri, Rajeswari, Yuzbasi, Suayip. (1402). 'Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations', سامانه مدیریت نشریات علمی, 11(3), pp. 589-604. doi: 10.22034/cmde.2022.51962.2170
Thirumalai, Sagithya, Seshadri, Rajeswari, Yuzbasi, Suayip. Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations. سامانه مدیریت نشریات علمی, 1402; 11(3): 589-604. doi: 10.22034/cmde.2022.51962.2170

Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations

Computational Methods for Differential Equations
مقاله 11، دوره 11، شماره 3، شهریور 2023، صفحه 589-604    اصل مقاله (421.15 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.51962.2170
نویسندگان
Sagithya Thirumalai* 1؛ Rajeswari Seshadri2؛ Suayip Yuzbasi3
1School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Tamil Nadu, India.
2Department of Mathematics, Pondicherry University, Puducherry, India.
3Department of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey.
چکیده
In this paper, a spectral collocation method for solving nonlinear pantograph type delay differential equations is presented. The basis functions used for the spectral analysis are based on Chebyshev, Legendre, and Jacobi polynomials. By using the collocation points and operations matrices of required functions such as derivative functions and delays of unknown functions, the method transforms the problem into a system of nonlinear algebraic equations. The solutions of this nonlinear system determine the coefficients of the assumed solution. The method is explained by numerical examples and the results are compared with the available methods in the literature. It is seen from the applications that our method gives more efficient results than that of the reported methods.
کلیدواژه‌ها
Nonlinear pantograph equations؛ Collocation method؛ Spectral method
مراجع
  • [1] E. Ashpazzadeh, M. Lakestani, and A. Fatholahzadeh, Spectral Methods Combined with Operational Matrices for Fractional Optimal Control Problems: A Review, Applied and computational mathematics, 20(2) (2021), 209-235.
  • [2] M.M. Bahsi, M. Cevik, and M. Sezer, Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation, Applied Mathematics and Computation, 271 (2015), 11-21.
  • [3] S. Davaeifar and J. Rashidinia, Solution of a system of delay differential equations of multi pantograph type, Journal of Taibah University for Science, 11(6) (2017), 1141-57.
  • [4] H. Dehestani, Y. Ordokhani, and M. Razzaghi, Numerical technique for solving fractional generalized pantograph- delay differential equations by using fractional-order hybrid bessel functions, International Journal of Applied and Computational Mathematics, 6(1) (2020), 1-27.
  • [5] E.H. Doha, A.H.Bhrawy, D. Baleanu, and R.M. Hafez, A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations, Applied Numerical Mathematics, 77 (2014), 43-54.
  • [6] T. Griebel, The pantograph equation in quantum calculus , Missouri University of Science and Technology, (2017).
  • [7] S. Gumgum, N. Baykus Savasaneril, O. K. Kurkcu, and M. Sezer, Lucas polynomial solution of nonlinear differ- ential equations with variable delays, Hacettepe Journal Of Mathematics And Statistics, (2019), 1-12.
  • [8] S. Gumgum, D. E. Ozdek, G. Ozaltun, and N. Bildik, Legendre wavelet solution of neutral  differential  equations  with proportional delays, Journal of Applied Mathematics and Computing, 6(1) (2019), 1-6.
  • [9] M. S. Hashemi, E. Ashpazzadeh, M. Moharrami, and M. Lakestani, Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type, Applied Numerical Mathematics, 170 (2021), 1-13.
  • [10] A. Isah and C. Phang, Operational matrix based on Genocchi polynomials for solution of delay differential equa- tions, Ain Shams Engineering Journal, 9(4) (2018).
  • [11] O. R. Isik, Z. Guney, and M. Sezer, Bernstein series solutions of pantograph equations using polynomial interpo-  lation, Journal of Difference Equations and Applications, 18(3) (2012), 357-374.
  • [12] J. P. Jaiswal, and K. Yadav, A comparative study of numerical solution of  pantograph  equations  using  various wavelets techniques, Journal of Applied and Engineering Mathematics, 11(3) (2021), 772-788.
  • [13] S. Javadi, E. Babolian, and Z. Taheri, Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials, Journal of Computational and Applied Mathematics, 303 (2016), 1-4.
  • [14] H. Jafari, M. Mahmoudi, and M. H. Noori Skandari, A new numerical method to solve pantograph delay differential equations with convergence analysis, Advances in Difference Equations, 2021(1) (2021), 1-12.
  • [15] M. Khasi, J. Rashidinia, and M. N. Rasoulizadeh, Computational Approaches to Solve the Nonlinear Acoustic Wave Equation Via a Bilinear Pseudo-Spectral Method, SSRN 3951006 (2021).
  • [16] F. Kong and R. Sakthivel, Uncertain external perturbation and mixed time delay impact on fixed-time synchro-  nization of discontinuous neutral-type neural networks, Applied and Computational Mathematics, 20(2) (2021), 290-312.
  • [17] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, (1993).
  • [18] N. MacDonald, Biological Delay Systems: Linear Stability Theory, Cambridge University Press, Cambridge, (1989).
  • [19] M. Molavi-Arabshahi and K. havali-koohshoori, Application of cubic B-spline collocation method for reaction diffusion Fisher’s equation, Computational Methods for Differential Equations, 9 (1) (2021), 22-35.
  • [20] J. R. Ockendon and A. B. Tayler, The dynamics of a current collection system for an electric locomotive, Proc.  R. Soc. Lond. A, 322 (1971), 447468.
  • [21] Y. Ozturk and M. Gulsu, Approximate solution of generalized pantograph equations with variable coefficients by operational method, An International Journal of Optimization and Control: Theories and Applications (IJOCTA), 7(1) (2016), 66-74.
  • [22] P. Rahimkhani, Y. Ordokhani, and E. Babolian, Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet, Journal of Computational and Applied Mathematics, 309 (2017), 493-510.
  • [23] P. Rahimkhani, Y. Ordokhani, and E. Babolian, A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations, Numerical Algorithms, 74(1) (2017), 223-45.
  • [24] J. Rashidinia, T. Eftekhari, and K. Maleknejad, Numerical solutions of two-dimensional nonlinear fractional Volterra and Fredholm integral equations using shifted Jacobi operational matrices via collocation method, Journal of King Saud University-Science, 33(1) (2021), 101244.
  • [25] M. Razavi, M. M. Hosseini, and  A.  Salemi,  Error  analysis  and  Kronecker  implementation  of  Chebyshev  spec-  tral collocation method for solving linear PDEs, Computational Methods for Differential Equations, DOI: 10.22034/CMDE.2021.46776.1966
  • [26] L. F.Shampine and P. Gahinet, Delay-differential-algebraic equations in control theory, Applied Numerical Math- ematics, 56 (2006), 574-578.
  • [27] L. P. Wang, Y. M. Chen, D. Y. Liu, and D. Boutat, Numerical algorithm to solve generalized fractional pantograph equations with variable coefficients based on shifted Chebyshev polynomials, International Journal of Computer Mathematics, 96(12) (2019), 2487-2510.
  • [28] C. Yang, Modified Chebyshev collocation method for pantograph-type differential equations, Applied Numerical Mathematics, 134 (2018), 132-44.
  • [29] C. Yang and J. Hou, Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations, Numerical Algorithms, 86(3) (2021), 1089-1108.
  • [30] S. Yuzbasi and N. Ismailov, A Taylor operation method for solutions of generalized  pantograph  type  delay  differential equations, Turkish Journal of Mathematics, 42(2) (2018), 395-406.
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