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Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh. (1401). Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems. سامانه مدیریت نشریات علمی, 10(4), 942-953. doi: 10.22034/cmde.2021.40288.1758
Saeid Abbasbandy; Hussein Sahihi; Tofigh Allahviranloo. "Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems". سامانه مدیریت نشریات علمی, 10, 4, 1401, 942-953. doi: 10.22034/cmde.2021.40288.1758
Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh. (1401). 'Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems', سامانه مدیریت نشریات علمی, 10(4), pp. 942-953. doi: 10.22034/cmde.2021.40288.1758
Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh. Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems. سامانه مدیریت نشریات علمی, 1401; 10(4): 942-953. doi: 10.22034/cmde.2021.40288.1758

Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems

Computational Methods for Differential Equations
مقاله 8، دوره 10، شماره 4، دی 2022، صفحه 942-953    اصل مقاله (611.92 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.40288.1758
نویسندگان
Saeid Abbasbandy* 1؛ Hussein Sahihi2؛ Tofigh Allahviranloo3
1Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34149-16818, Iran.
2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey.
چکیده
In this paper, a reliable new scheme is presented based on combining Reproducing Kernel Method (RKM) with a practical technique for the nonlinear problem to solve the System of Singularly Perturbed Boundary Value Problems (SSPBVP). The Gram-Schmidt orthogonalization process is removed in the present RKM. However, we provide error estimation for the approximate solution and its derivative. Based on the present algorithm in this paper, can also solve linear problem. Several numerical examples demonstrate that the present algorithm does have higher precision. 
کلیدواژه‌ها
Reproducing kernel method؛ Singularly perturbed BVPs؛ Convergence analysis؛ Error analysis؛ System of differential equations
مراجع
  • [1]          S. Abbasbandy, H. Sahihi, and T. Allahviranloo, Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems, Math. Model. Anal., 26 (2021), 116–134.
  • [2]          A. Akgu¨l, M. Inc, and E. Karatas, Reproducing Kernel Functions for Difference Equations, Disc. Cont. Dynam. System. Serie. S., 8 (2015), 1055–1064.
  • [3]          A.  Akgu¨l,  M.  Inc,  E.  Karatas,  and  D.  Baleanu,  Numerical  solutions  of  fractional  differential  equations  of  Lane- Emden type by an accurate technique, Advan. Diff. Equ., 220 (2015), 1–12.
  • [4]          A. Akgu¨l, E. K. Akgu¨l, D. Baleanu, and M. Inc, New Numerical Method for Solving Tenth Order Boundary Value Problems, Math., 6 (2018), 1–9.
  • [5]          E. K. Akgu¨l, A. Akgu¨l, Y. Khan, and D. Baleanu, Representation for the reproducing kernel Hilbert space method for a nonlinear system, Math. Statis., 3 (2019), 1345–1355.
  • [6]          A. Akgu¨l and E. K. Akgu¨l, A Novel Method for Solutions of Fourth-Order Fractional Boundary Value Problems, Fractal. Fractional., 3 (2019), 1–13.
  • [7]          A.  Akgu¨l,  E.  K.  Akgu¨l,  and  S.  Korhan,  A  New  reproducing  kernel  functions  in  the  reproducing  kernel  Sobolev spaces, AIMS. Math., 5 (2020), 482–496.
  • [8]          T. Allahviranloo and H. Sahihi, Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions, Num. Method. Partial. Diff. Equ., 36 (2020), 1758–1772.
  • [9]          T. Allahviranloo and H. Sahihi, Reproducing kernel method to solve fractional delay differential equations, Appl. Math. Comput., 400 (2021), 126095.
  • [10]        K. Atkinson and W. Han, Theoretical Numerical Analysis A Functional Analysis Framework, Third Edition, Springer Science, New York, USA, (2009).
  • [11]        E. Babolian, S. Javadi, and E. Moradi, Error analysis of reproducing kernel Hilbert space method for solving functional integral equations, J. Comput. Appl. Math., 300 (2016), 300–311.
  • [12]        E. Babolian and D. Hamedzadeh, A splitting iterative method for solving second kind integral equations in repro- ducing kernel spaces, J. Comput. Appl. Math., 326 (2017), 204–216.
  • [13]        Z. Chen and Z. J. Chen, The exact solution of system of linear operator equations in reproducing kernel spaces,  Appl. Math. Comput., 203 (2008), 56–61.
  • [14]        M. Cui and Y. Lin Nonlinear numerical analysis in the reproducing kernel space, Nova Science, Hauppauge, New York, United States, (2009).
  • [15]        P. Das and S. Natesan, Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems, Appl. Math. Comput., 249 (2014), 265–277.
  • [16]        F. Z. Geng and M. G. Cui, Solving a nonlinear system of second order boundary value  problems,  J. Math. Anal.  Appl., 327 (2007), 1167–1181.
  • [17]        R. K. Ghaziani, M. Fardi, and M. Ghasemi, Solving multi-order fractional differential equations by reproducing kernel Hilbert space method, Comput. Method. Diff. Equ., 4 (2016), 170–190.
  • [18]        W. Jiang and Z. Chen, solving a system of linear Volterra integral equations using the new reproducing kernel method, Appl. Math. Comput., 219 (2013), 10225–10230.
  • [19]        Y. Kan-On and M. Mimura, Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics, SIAM. J. Math. Anal., 29 (1998), 1519–1536.
  • [20]        R. Ketabchi, R. Mokhtari, and E. Babolian, Some error estimates for solving Volterra integral equations by using the reproducing kernel method, J. Comput. Appl. Math., 273 (2015), 245–250.
  • [21]        X. Li, Y. Gao, and B. Wu, Mixed reproducing kernel-based iterative approach for nonlinear boundary value problems with nonlocal conditions, Comput. Method. Diff. Equ., 9(3) (2020), 649-658, DOI: 10.22034/CMDE.2020.38153.1681.
  • [22]        Y. Z. lin, Y. L. Wang, F. G. Tan, X. H. Wan, H. Yu, and J. S. Duan, Solving a class of linear nonlocal boundary value problems using the reproducing kernel, Appl. Math. Comput., 265 (2015), 1098–1105.
  • [23]        X. Lu and M. G. Cui, Solving a singular system of two nonlinear ODEs, Appl. Math. Comput., 198 (2008), 534–543.
  • [24]        N. Madden, M. Stynes, and G. P. Thomas, On the application of robust numerical methods to a complete-flow wave-current model, in: Boundary and Interior Layers (BAIL), Toulouse, Hauppauge, New York, United States, (1998).
  • [25]        L. Mei and Y. Lin, Simplified reproducing kernel method and convergence order for linear Volterra integral equa- tions with variable coefficients, J. Comput. Appl. Math., 346 (2019), 390–398.
  • [26]        S. Matthews, E. O’Riordan, and G. I. Shishkin, A numerical method for a system of singularly perturbed reaction-  diffusion equations, J. Comput. Appl. Math., 145 (2002), 151–166.
  • [27]        D.S. Naidu and K. A. Rao, Singular perturbation analysis of the closed-loop discrete optimal control problem, Opt. Cont. Appl. Method., 5 (1984), 19–37.
  • [28]        S. Natesan and N. Ramanujam, A booster method for singular perturbation problems arising in chemical reactor theory by incorporation of asymptotic approximations, Appl. Math. Comput., 100 (1999), 27–48.
  • [29]        S. Natesan and B. S. Deb, A robust computational method for singularly perturbed coupled system of reaction- diffusion boundary-value problems, Appl. Math. Comput., 188 (2007), 353–364.
  • [30]        W. H. Ruan and C. V. Pao, Asymptotic behavior and positive solutions of a chemical reaction  diffusion system,   J. Math. Anal. Appl., 159 (1992), 157–178.
  • [31]        H. Sahihi, S. Abbasbandy, and T. Allahviranloo, Reproducing kernel method for solving singularly perturbed differential-difference equations with boundary layer behavior in Hilbert  space,  J.  Comput.  Appl.  Math.,  328  (2018), 30–43.
  • [32]        H. Sahihi, S. Abbasbandy, and T. Allahviranloo, Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay, Appl. Math. Comput., 361 (2019), 583–598.
  • [33]        H. Sahihi,  T. Allahviranloo,  and S. Abbasbandy,  Solving system of second-order  BVPs using a new algorithm   based on reproducing kernel Hilbert space, Appl. Num. Math., 151 (2020), 27–39.
  • [34]        N. Sharp and M. Trummer, A Spectral Collocation Method for Systems of Singularly Perturbed Boundary Value Problems, Proc. Comput. Sci., 1080 (2017), 725–734.
  • [35]        Y. Wang, T. Chaolu, and P. Jing, New algorithm for second-order boundary value problems of integro-differential equation, J. Comput. Appl. Math., 229 (2009), 1–6.
  • [36]        Y. Wang, L. Su, X. Cao, and X. Li, Using reproducing kernel for solving a class of singularly perturbed problems, Comput. Math. Appl., 61 (2011), 421–430.
  • [37]        Y. Wang, L. Su, and Z. Chen, Using reproducing kernel for solving a class of singular weakly nonlinear boundary value problems, Int. J. Comput. Math., 87 (2010), 367–380.
  • [38]        L. H. Yang, J. H. Shen, and Y. Wang, The reproducing kernel method for solving the system of the linear Volterra integral equations with variable coefficients, J. Comput. Appl. Math., 236 (2012), 2398–2405.
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