Araştırma Makalesi
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A New Transformation Method for Solving High-Order Boundary Value Problems

Yıl 2022, Sayı: 40, 90 - 100, 30.09.2022
https://doi.org/10.53570/jnt.1171760

Öz

The main purpose of this work is to provide a new approximation method, the so-called parameterised differential transform method (PDTM), for solving high-order boundary value problems (HOBVPs). Our method is based on the classical differential transform method and differs from it by calculating the coefficients of the solution, which has the form of a series. We applied the proposed new method to fourth-order boundary value problems to substantiate it. The resulting solution is graphically compared with the exact solution and the solutions obtained by the classical DTM and ADM methods.

Kaynakça

  • J. K. Zhou, Differential Transformation and Its Application for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  • S. Momani, M. A. Noor, Numerical Comparison of Methods for Solving a Special Fourth-Order Boundary Value Problem, Applied Mathematics and Computation, 191 (1) (2007) 218–224.
  • I. A. H. Hassan, V. S. Erturk, Solutions of Different Types of the Linear and Nonlinear Higher-Order Boundary Value Problems by Differential Transformation Method, European Journal of Pure and Applied Mathematics 2 (3) (2009) 426–447.
  • C. H. Che Hussin, A. Kiliçman, On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method, Mathematical problems in engineering (2011).
  • E. R. El-Zahar, Approximate Analytical Solutions of Singularly Perturbed Fourth Order Boundary Value Problems Using Differential Transform Method, Journal of king Saud university-science 25 (3) (2013) 257–265.
  • V. S. Ertürk, S. Momani, Comparing Numerical Methods for Solving Fourth-Order Boundary Value Problems, Applied Mathematics and Computation 188 (2) (2007) 1963–1968.
  • A. M. Wazwaz, The Numerical Solution of Special Fourth-Order Boundary Value Problems by the Modified Decomposition Method, International journal of computer mathematics 79 (3) (2002) 345–356.
  • D. Arslan, Approximate Solutions of the Fourth-Order Eigenvalue Problem, Journal of Advanced Research in Natural and Applied Sciences 8 (2) (2022) 214–221.
  • O. Mukhtarov, M. Yücel, K. Aydemir, A New Generalization of the Differential Transform Method for Solving Boundary Value Problems, Journal of New Results in Science 10 (2) (2021) 49–58.
  • O. Mukhtarov, M. Yücel, K. Aydemir, Treatment a New Approximation Method and its Justification for Sturm–Liouville Problems, Complexity Article ID 8019460 (2020) 8 Pages.
  • O. Mukhtarov, S. Çavuşoğlu, H. Olğar, Numerical Solution of One Boundary Value Problem Using Finite Difference Method, Turkish Journal of Mathematics and Computer Science 11 (2019) 85–89.
  • B. Boukary, J. Loufouilou-Mouyedo, J. Bonazebi-Yindoula, G. Bissanga, Application of the Adomian Decomposition Method (ADM) for Solving the Singular Fourth-Order Parabolic Partial differential equation, Journal of Applied Mathematics and Physics 6 (07) (2018) 14–76.
  • A. Kwami, M. Salisu, J. Hussaini, M. Garba, Modified Adomian Decomposition Method for the Solution of Fourth Order Ordinary Differential Equations, GSJ 8(4) (2020).
  • O. S. Mukhtarov, M. Yücel, A Study of the Eigenfunctions of the Singular Sturm–Liouville Problem Using the Analytical Method and the Decomposition Technique, Mathematics 8 (3) (2020) 415.
  • A. Rysak, M. Gregorczyk, Differential Transform Method as an Effective Tool for investigating fractional dynamical systems, Applied Sciences 11 (15) (2021), 69–55.
  • M. Yücel, O. S. Mukhtarov, A New Treatment of the Decomposition Method for Nonclassical Boundary Value Problems, Journal of Advanced Physics 7 (2) (2018), 161–166.
  • A. S. J. Al-Saif, A. J. Harfash, A Comparison Between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations, Journal of Applied Mathematics and Physics 6 (12) (2018), 2518–2543.
  • J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, A Review of the Adomian Decomposition Method and its Applications to Fractional Differential Equations, Communications in Fractional Calculus, 3 (2) (2012), 73–99.
  • F. Ayaz, Solutions of the System of Differential Equations by Differential Transform Method, Applied Mathematics and Computation, 147 (2) (2004), 547–567.
Yıl 2022, Sayı: 40, 90 - 100, 30.09.2022
https://doi.org/10.53570/jnt.1171760

Öz

Kaynakça

  • J. K. Zhou, Differential Transformation and Its Application for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  • S. Momani, M. A. Noor, Numerical Comparison of Methods for Solving a Special Fourth-Order Boundary Value Problem, Applied Mathematics and Computation, 191 (1) (2007) 218–224.
  • I. A. H. Hassan, V. S. Erturk, Solutions of Different Types of the Linear and Nonlinear Higher-Order Boundary Value Problems by Differential Transformation Method, European Journal of Pure and Applied Mathematics 2 (3) (2009) 426–447.
  • C. H. Che Hussin, A. Kiliçman, On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method, Mathematical problems in engineering (2011).
  • E. R. El-Zahar, Approximate Analytical Solutions of Singularly Perturbed Fourth Order Boundary Value Problems Using Differential Transform Method, Journal of king Saud university-science 25 (3) (2013) 257–265.
  • V. S. Ertürk, S. Momani, Comparing Numerical Methods for Solving Fourth-Order Boundary Value Problems, Applied Mathematics and Computation 188 (2) (2007) 1963–1968.
  • A. M. Wazwaz, The Numerical Solution of Special Fourth-Order Boundary Value Problems by the Modified Decomposition Method, International journal of computer mathematics 79 (3) (2002) 345–356.
  • D. Arslan, Approximate Solutions of the Fourth-Order Eigenvalue Problem, Journal of Advanced Research in Natural and Applied Sciences 8 (2) (2022) 214–221.
  • O. Mukhtarov, M. Yücel, K. Aydemir, A New Generalization of the Differential Transform Method for Solving Boundary Value Problems, Journal of New Results in Science 10 (2) (2021) 49–58.
  • O. Mukhtarov, M. Yücel, K. Aydemir, Treatment a New Approximation Method and its Justification for Sturm–Liouville Problems, Complexity Article ID 8019460 (2020) 8 Pages.
  • O. Mukhtarov, S. Çavuşoğlu, H. Olğar, Numerical Solution of One Boundary Value Problem Using Finite Difference Method, Turkish Journal of Mathematics and Computer Science 11 (2019) 85–89.
  • B. Boukary, J. Loufouilou-Mouyedo, J. Bonazebi-Yindoula, G. Bissanga, Application of the Adomian Decomposition Method (ADM) for Solving the Singular Fourth-Order Parabolic Partial differential equation, Journal of Applied Mathematics and Physics 6 (07) (2018) 14–76.
  • A. Kwami, M. Salisu, J. Hussaini, M. Garba, Modified Adomian Decomposition Method for the Solution of Fourth Order Ordinary Differential Equations, GSJ 8(4) (2020).
  • O. S. Mukhtarov, M. Yücel, A Study of the Eigenfunctions of the Singular Sturm–Liouville Problem Using the Analytical Method and the Decomposition Technique, Mathematics 8 (3) (2020) 415.
  • A. Rysak, M. Gregorczyk, Differential Transform Method as an Effective Tool for investigating fractional dynamical systems, Applied Sciences 11 (15) (2021), 69–55.
  • M. Yücel, O. S. Mukhtarov, A New Treatment of the Decomposition Method for Nonclassical Boundary Value Problems, Journal of Advanced Physics 7 (2) (2018), 161–166.
  • A. S. J. Al-Saif, A. J. Harfash, A Comparison Between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations, Journal of Applied Mathematics and Physics 6 (12) (2018), 2518–2543.
  • J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, A Review of the Adomian Decomposition Method and its Applications to Fractional Differential Equations, Communications in Fractional Calculus, 3 (2) (2012), 73–99.
  • F. Ayaz, Solutions of the System of Differential Equations by Differential Transform Method, Applied Mathematics and Computation, 147 (2) (2004), 547–567.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Araştırma Makalesi
Yazarlar

Merve Yücel 0000-0001-7990-2821

Fahreddin Muhtarov 0000-0002-5482-2478

Oktay Mukhtarov 0000-0001-7480-6857

Yayımlanma Tarihi 30 Eylül 2022
Gönderilme Tarihi 6 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Sayı: 40

Kaynak Göster

APA Yücel, M., Muhtarov, F., & Mukhtarov, O. (2022). A New Transformation Method for Solving High-Order Boundary Value Problems. Journal of New Theory(40), 90-100. https://doi.org/10.53570/jnt.1171760
AMA Yücel M, Muhtarov F, Mukhtarov O. A New Transformation Method for Solving High-Order Boundary Value Problems. JNT. Eylül 2022;(40):90-100. doi:10.53570/jnt.1171760
Chicago Yücel, Merve, Fahreddin Muhtarov, ve Oktay Mukhtarov. “A New Transformation Method for Solving High-Order Boundary Value Problems”. Journal of New Theory, sy. 40 (Eylül 2022): 90-100. https://doi.org/10.53570/jnt.1171760.
EndNote Yücel M, Muhtarov F, Mukhtarov O (01 Eylül 2022) A New Transformation Method for Solving High-Order Boundary Value Problems. Journal of New Theory 40 90–100.
IEEE M. Yücel, F. Muhtarov, ve O. Mukhtarov, “A New Transformation Method for Solving High-Order Boundary Value Problems”, JNT, sy. 40, ss. 90–100, Eylül 2022, doi: 10.53570/jnt.1171760.
ISNAD Yücel, Merve vd. “A New Transformation Method for Solving High-Order Boundary Value Problems”. Journal of New Theory 40 (Eylül 2022), 90-100. https://doi.org/10.53570/jnt.1171760.
JAMA Yücel M, Muhtarov F, Mukhtarov O. A New Transformation Method for Solving High-Order Boundary Value Problems. JNT. 2022;:90–100.
MLA Yücel, Merve vd. “A New Transformation Method for Solving High-Order Boundary Value Problems”. Journal of New Theory, sy. 40, 2022, ss. 90-100, doi:10.53570/jnt.1171760.
Vancouver Yücel M, Muhtarov F, Mukhtarov O. A New Transformation Method for Solving High-Order Boundary Value Problems. JNT. 2022(40):90-100.


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