Dergiler / Fundamental Journal of Mathematics and Applications / 2020 / Cilt: 3 Sayı: 2

On Solutions of a Higher Order Nonhomogeneous Ordinary Differential Equation

Sayfa
153–160
Yayın Tarihi
2020-12-15
DOI
—
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Absolute errors and relative errors have been given in the tables.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Higher order differential equations (ODE) has an important role in the modelling process.
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Temel Bulgular & Veri:It is also much significant which the method is used for the solution.
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Sonuç & Katkı:Absolute errors and relative errors have been given in the tables.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nonhomogeneous ordinary differential equations · Approximate solution · Initial value problems Reproducing kernel method

Abstract

Higher order differential equations (ODE) has an important role in the modelling process. It is also much significant which the method is used for the solution. In this study, in order to get the approximate solution of a nonhomogeneous initial value problem, reproducing kernel Hilbert space method is used. Reproducing kernel functions have been obtained and the given problem transformed to the homogeneous form. The results have been presented with the graphics. Absolute errors and relative errors have been given in the tables.

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Bu Makaleye Atıf Yap

YILDIRIM, E. N., AKGUL, A. (2020). On Solutions of a Higher Order Nonhomogeneous Ordinary Differential Equation. Fundamental Journal of Mathematics and Applications, Cilt: 3 Sayı: 2, 153–160. https://ajindex.com/articles/905718

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Kaynakça (17)

  1. N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404
  2. S. Bergman, The Kernel Function and Conformal Mapping, American Math. Soc., New York, (1950)
  3. M. Cui, Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, New York: Nova Sci. Publ., (2009)
  4. M. I. Syam, Q. M. Al-Mdallal and M. Al-Refai, A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems, Com. in Num. Analy., 2 (2017), 217–232
  5. W. Jiang, T. Tian, Numerical solution of nonlinear Volterra integro-differential equations of fractional order by the reproducing kernel method, App. Math. Mod., 39 (16) (2015), 4871–4876
  6. X. Y. Li, B. Y. Wu, R. T. Wan, Reproducing Kernel Method for Fractional Riccati Differential Equations, Abst. App. Ana., (2014), 1-6
  7. A. Alvandi, M. Paripour, The combined reproducing kernel method and Taylor series to solve nonlinear Abel’s integral equations with weakly singular kernel, Cogent Mathematics, 3 (2016)
  8. A. Freihat, R. Abu-Gdairi, H. Khalil, E. Abuteen, M. Al-Smadi, R. A. Khan, Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems, American J. App. Sci., 13 (2016), 501–510
  9. G. Akram, H. U. Rehman, Numerical solution of eighth order boundary value problems in reproducing Kernel space, Numer. Algor, 62(3) (2013), 527–540
  10. S. Abbasbandy, Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian’s decomposition method, Appl. Math. Comput, 172 (2006), 485–490
  11. G. Adomian, Nonlinear Stochastic Operator Equations, Academic Press, San Diego, (1986)
  12. A. Daşcıoğlu, H. Yaslan, The solution of high-order nonlinear ordinary differential equations by Chebshev series, Appl. Math. Comput., 217 (2011), 5658–5666
  13. A.M. Wazwaz, A new method for solving initial value problems in second-order ordinary differential equations, Appl. Math. Comput., 128 (2002), 45–57
  14. M. K. Horn, Fourth- and fifth-order, scaled Runge-Kutta algorithms for treating dense output, SI AM J. Numer. Analysis, 20 (1983), 558-568
  15. L. Fox, D. F. Mayers, Numerical Solution of Ordinary Differential Equations, Chapman and Hall, (1987)
  16. A.M. Wazwaz, The numerical solution of fifth-order boundary value problems by the decomposition method, J. Comput. Appl. Math. 136(1–2) (2001), 259–270
  17. Waeleh et al., Numerical Solution of Higher Order Ordinary Differential Equations by Direct Block Co