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Dehbozorgi, Raziyeh, Ebrahimzadeh, Asiyeh. (1403). An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations. سامانه مدیریت نشریات علمی, 12(1), 77-88. doi: 10.22034/cmde.2023.55213.2295
Raziyeh Dehbozorgi; Asiyeh Ebrahimzadeh. "An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations". سامانه مدیریت نشریات علمی, 12, 1, 1403, 77-88. doi: 10.22034/cmde.2023.55213.2295
Dehbozorgi, Raziyeh, Ebrahimzadeh, Asiyeh. (1403). 'An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations', سامانه مدیریت نشریات علمی, 12(1), pp. 77-88. doi: 10.22034/cmde.2023.55213.2295
Dehbozorgi, Raziyeh, Ebrahimzadeh, Asiyeh. An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations. سامانه مدیریت نشریات علمی, 1403; 12(1): 77-88. doi: 10.22034/cmde.2023.55213.2295

An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations

Computational Methods for Differential Equations
مقاله 7، دوره 12، شماره 1، فروردین 2024، صفحه 77-88    اصل مقاله (383.48 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55213.2295
نویسندگان
Raziyeh Dehbozorgi1؛ Asiyeh Ebrahimzadeh* 2
1Iran University of science and technology, Tehran, Iran.
2Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.
چکیده
In this paper, we introduce an operational vector approach that uses Chebyshev wavelets and hybrid functions to approximate the solution of the Riccati differential equation arising in nonlinear physics equations celebrated as cosmology problems. The scheme's main features include a simple structure based on certain matrices and vectors, low computational complexity, and high accuracy. The method is direct, which means that projection methods are not used throughout the approximation procedure in order to reduce computational cost. Error analyses are provided, and several numerical examples and comparisons confirm the proposed scheme's superiority.
کلیدواژه‌ها
Riccati equation؛ Direct method؛ Chebyshev wavelets؛ Hybrid functions؛ Operational vectors
مراجع
  • [1] P.  Assari and M. Dehghan, The numerical solution of nonlinear weakly singular fredholm  integral  equations based     on the dual-chebyshev wavelets, Applied and computational mathematics, 19(1) (2020), 3-19.
  • [2] E. Babolian and F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet opera- tional matrix of integration, Applied Mathematics and computation, 188(1) (2007), 417-426.
  • [3] E. Babolian and Z. Masouri, Direct method to solve Volterra integral equation of the first  kind  using  operational matrix with block-pulse functions, Journal of Computational and Applied Mathematics, 220(1-2) (2008), 51-57.
  • [4] P. P.Boyle, W. Tian, and F. Guan, The Riccati equation in mathematical finance, Journal of Symbolic Computa- tion,33(3) (2002), 343-355.
  • [5] M. Y. Hussaini and T. A. Zang, Spec tral methods in fluid dynamics, Annual review of fluid mechanics, 19(1) (1987), 339-367.
  • [6] V. Christianto and S. V. Ershkov, Two Applications of Riccati  ODE in Nonlinear Physics and Their Computer  Algebra Solutions, Victor Christianto— Florentin Smarandache, 2(2018), 132.
  • [7] F. Cooper, A. Khare, and U. Sukhatme, Supersymmetry and quantum mechanics, Physics Reports, 251(5-6) (1995), 267-385.
  • [8]K. B. Datta and B. A. Mohan, Orthogonal functions in systems and control, World Scientific, 9 (1995).
  • [9] R. Dehbozorgi and K. Maleknejad, Direct numerical scheme for  all classes  of  nonlinear  Volterra  integral  equations of the first kind, (2018) arXiv preprint arXiv:1808.03906.
  • [10] B. Hasani lichae, J. Biazar, and Z. Ayati, Asymptotic decomposition method for fractional order Riccati differential equation, Computational Methods for Differential Equations, 9(1) (2021), 63-78.
  • [11] H. Jafari, S. A. Yousefi, M. A. Firoozjaee, S. Momani, and C. M. Khalique, Application of Legendre wavelets for solving fractional differential equations, Computers and Mathematics with Applications, 62(3) (2011), 1038-1045.
  • [12] Z. Jiang and W. Schaufelberger, Block pulse functions and their applications in control systems, Berlin: Springer- Verlag, 179 (1992).
  • [13] M. D. Johansyah, A. K. Supriatna, E. Rusyaman, and J. Saputra, The Existence and Uniqueness of Riccati Frac- tional Differential Equation Solution and Its Approximation Applied to an Economic Growth Model, Mathematics, 10(17) (2022), 3029.
  • [14]  E. Keshavarz, Y. Ordokhani, and M. Razzaghi, Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Applied Mathematical Modelling, 38(24) (2014), 6038-6051.
  • [15] M. Lakestani and M. Dehghan, Numerical solution of Riccati equation using the  cubic  B-spline  scaling  functions  and Chebyshev cardinal functions, Computer Physics Communications, 181(5) (2010), 957-966.
  • [16] K. Maleknejad, S. Sohrabi, and Y. Rostami, Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials, Applied Mathematics and Computation, 188(1) (2007), 123-128.
  • [17] K. Maleknejad and R. Dehbozorgi, Adaptive numerical approach based upon Chebyshev operational vector for nonlinear Volterra integral equations and its convergence analysis, Journal of Computational and Applied Math- ematics, 344(2018), 356-366.
  • [18] K. Maleknejad, R. Dehbozorgi, and M. Garshasbi, Direct operational matrix approach for weakly singular Volterra integro-differential equations: application in theory of anomalous diffusion, Mathematical Comnications, 24(1) (2019), 61-76.
  • [19] K. Maleknejad and E. Hashemizadeh, A numerical approach for Hammerstein integral equations of mixed type using operational matrices of hybrid functions, Sci. Bull.“Politeh.” Univ. Buchar., Ser. A, Appl. Math. Phys, 73 (2011), 95-104.
  • [20] K. Maleknejad, M.  Khodabin,  and  M.  Rostami  Numerical  solution  of  stochastic  Volterra  integral  equations  by a stochastic operational matrix based on block pulse functions, Mathematical and computer Modelling, 55(3-4) (2012), 791-800.
  • [21] K. Maleknejad, S. Sohrabi and Y. Rostami, Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials, Applied Mathematics and Computation, 188(1) (2007), 123-128.
  • [22] V. B. Matveev and M. A. Salle, Darboux transformations and solitons,. Berlin: Springer, 17 (1991).
  • [23] K. A. Milton, S. D. Odintsov, and S. Zerbini, Bulk versus brane running couplings, Physical Review D, 65(6) (2002), 065012.
  • [24] M. Nowakowski and H. C. Rosu, Newton’s laws of motion in the form of a Riccati equation, Physical Review E, 65(4) (2002), 047602.
  • [25] K. Nedaiasl and R. Dehbozorgi, Galerkin finite element method for nonlinear fractional differential equations, Numerical Algorithms, 88(1) (2021), 113-141.
  • [26] Z. Odibat and S. Momani, Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos, Solitons and Fractals,36(1) (2008), 167-174.
  • [27] Y.Öztürk and M. Gülsu, Numerical solution of Riccati equation using operational matrix method with Chebyshev polynomials, Asian-European Journal of Mathematics, 8(02) (2015), 1550020.
  • [28] J. Prüss, Evolutionary integral equations and applications, Birkhäuser, 87 (2013).
  • [29] M. Razzaghi and H. R. Marzban, Direct method for variational problems via hybrid of block-pulse and Chebyshev functions, Mathematical problems in Engineering, 6(1) (2000), 85-97.
  • [30] M. R.Scott, Invariant imbedding and its applications to ordinary differential equations, An introduction, (1973).
  • [31] J. Singh, A. Gupta, and D. Kumar Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory, Mathematics, 11(3) (2023), 644.
  • [32] M. M. Shamooshaky, P. Assari, and H. Adibi The numerical solution of nonlinear Fredholm-Hammerstein integral equations of the second kind utilizing Chebyshev wavelets, J. Math. Comput. Sci., 10 (2014), 235-246.
  • [33] A. Toma, F. Dragoi, and O. Postavaru, Enhancing the accuracy of solving Riccati fractional differential equations, Fractal and Fractional, 6(5) (2022), 275.
  • [34]L. I. Yuanlu, Solving a nonlinear fractional differential equation using Chebyshev wavelets, Communications in Nonlinear Science and Numerical Simulation, 15(9) (2010), 2284-2292.
  • [35] S.  Yüzba¸sı,  Numerical  solutions  of  fractional  Riccati  type  differential  equations  by  means  of  the  Bernstein  poly- nomials, Applied Mathematics and Computation, 219(11) (2013), 6328-6343.
  • [36] M. I. Zelekin, Homogeneous spaces and Riccati equation in variational calculus. Factorial, Moscow, (1998).
  • [37] S. Vahdati, M. R. Ahmadi Darani, and M. R. Ghanei,Haar wavelet-based valuation method for pricing European options, Computational Methods for Differential Equations, 11(2) (2023), 281-290.
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