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Solution of Integro-Differential Difference equations via Differential Transform Method

Yıl 2021, Cilt: 18 Sayı: 1, 33 - 46, 01.05.2021

Öz

This study presents the application of semi-analytical and numerical solution technique to both Volterra and Fredholm integro-differential difference equations by employing Differential Transform Method depending on Taylor series expansion and introducing the new differential transform theorems with their proofs. To illustrate the computational efficiency and the reliability of the method to other common numerical methods in the open literature, some examples are carried out it is found that the results are highly accurate and reliable.

Kaynakça

  • [1] R. Abazari, A. Kilicman, “Application of differential transform method on nonlinear integro-differential equations with proportional delay,” Neural Computing and Applications, vol. 24, pp. 391–397, 2014.
  • [2] A. Arikoglu, I. Ozkol, “Solution of boundary value problems for integro-differential equations by using differential transform method,” Applied Mathematics and Computation, vol. 168, pp. 1145-1158, 2005.
  • [3] A. Arikoglu, I. Ozkol, “Solution of difference equations by using differential transform method,” Applied Mathematics and Computation, vol. 174, pp. 1216-1228, 2006.
  • [4] A. Arikoglu, I. Ozkol, “Solution of differential–difference equations by using differential transform method,” Applied Mathematics and Computation, vol. 181, pp. 153–162, 2006.
  • [5] A. Arikoglu, I. Ozkol, “Solution of fractional differential equations by using differential transform method,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1473–1481, 2007.
  • [6] A. Arikoglu, I. Ozkol, “Solutions of integral and integro-differential equation systems by using differential transform method,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2411–2417, 2008.
  • [7] A. Arikoglu, I. Ozkol, “Solution of fractional integro-differential equations by using fractional differential transform method,” Chaos, Solitons & Fractals, vol. 40, no. 2, pp. 521–529, 2009.
  • [8] F. Ayaz, “Solutions of the system of differential equations by differential transform method,” Applied Mathematics and Computation, vol. 147, pp. 547–567, 2004.
  • [9] M. M. Bahsi, A. K. Bahsi, M. Cevik, M. Sezer, “Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations,” Mathematical Sciences, vol. 10, pp. 83-93, 2016.
  • [10] M. Balci, M. Sezer, “Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations,” Applied Mathematics and Computation, vol. 273, pp. 33–41, 2016.
  • [11] F. Karakoc, H. Bereketoglu, “Solutions of delay differential equations by using differential transform method,” International Journal of Computer Mathematics, vol. 86, no. 5, pp. 914-923, 2009.
  • [12] Z. M. Odibat, “Differential transform method for solving Volterra integral equation with separable kernels,” Mathematical and Computer Modelling, vol. 8, no. 7-8, pp. 1144-1149, 2008.
  • [13] S. Y. Reutskiy, “The backward substitution method for multipoint problems with linear Volterra-Fredholm integro-differential equations of the neutral type,” Journal of Computational and Applied Mathematics, vol. 296, pp. 724-738, 2016.
  • [14] F.A. Rihan, E.H. Doha, M.I. Hassan, N.M. Kamel, “Numerical treatments for Volterra delay integro-differential equations,” Computational Methods in Applied Mathematics, vol. 9, no. 3, pp. 292–308, 2009. [15] A. Saatmandi, M. Dehghan, “Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients,” Computers & Mathematics with Applications, vol. 59, pp. 2996-3004, 2010.
  • [16] P. K. Sahu, S. S. Ray, “Legendre spectral collocation method for Fredholm integro-differential difference equation with variable coefficients and mixed conditions,” Applied Mathematics and Computation, vol. 268, pp. 575-580, 2015.
  • [17] S. Yuzbasi, “Laguerre approach for solving pantograph-type Volterra integro-differential equations,” Applied Mathematics and Computation, vol. 232, pp. 1183–1199, 2014.
  • [18] J.K. Zhou, Differential Transformation and Its Application for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986).
Yıl 2021, Cilt: 18 Sayı: 1, 33 - 46, 01.05.2021

Öz

Kaynakça

  • [1] R. Abazari, A. Kilicman, “Application of differential transform method on nonlinear integro-differential equations with proportional delay,” Neural Computing and Applications, vol. 24, pp. 391–397, 2014.
  • [2] A. Arikoglu, I. Ozkol, “Solution of boundary value problems for integro-differential equations by using differential transform method,” Applied Mathematics and Computation, vol. 168, pp. 1145-1158, 2005.
  • [3] A. Arikoglu, I. Ozkol, “Solution of difference equations by using differential transform method,” Applied Mathematics and Computation, vol. 174, pp. 1216-1228, 2006.
  • [4] A. Arikoglu, I. Ozkol, “Solution of differential–difference equations by using differential transform method,” Applied Mathematics and Computation, vol. 181, pp. 153–162, 2006.
  • [5] A. Arikoglu, I. Ozkol, “Solution of fractional differential equations by using differential transform method,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1473–1481, 2007.
  • [6] A. Arikoglu, I. Ozkol, “Solutions of integral and integro-differential equation systems by using differential transform method,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2411–2417, 2008.
  • [7] A. Arikoglu, I. Ozkol, “Solution of fractional integro-differential equations by using fractional differential transform method,” Chaos, Solitons & Fractals, vol. 40, no. 2, pp. 521–529, 2009.
  • [8] F. Ayaz, “Solutions of the system of differential equations by differential transform method,” Applied Mathematics and Computation, vol. 147, pp. 547–567, 2004.
  • [9] M. M. Bahsi, A. K. Bahsi, M. Cevik, M. Sezer, “Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations,” Mathematical Sciences, vol. 10, pp. 83-93, 2016.
  • [10] M. Balci, M. Sezer, “Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations,” Applied Mathematics and Computation, vol. 273, pp. 33–41, 2016.
  • [11] F. Karakoc, H. Bereketoglu, “Solutions of delay differential equations by using differential transform method,” International Journal of Computer Mathematics, vol. 86, no. 5, pp. 914-923, 2009.
  • [12] Z. M. Odibat, “Differential transform method for solving Volterra integral equation with separable kernels,” Mathematical and Computer Modelling, vol. 8, no. 7-8, pp. 1144-1149, 2008.
  • [13] S. Y. Reutskiy, “The backward substitution method for multipoint problems with linear Volterra-Fredholm integro-differential equations of the neutral type,” Journal of Computational and Applied Mathematics, vol. 296, pp. 724-738, 2016.
  • [14] F.A. Rihan, E.H. Doha, M.I. Hassan, N.M. Kamel, “Numerical treatments for Volterra delay integro-differential equations,” Computational Methods in Applied Mathematics, vol. 9, no. 3, pp. 292–308, 2009. [15] A. Saatmandi, M. Dehghan, “Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients,” Computers & Mathematics with Applications, vol. 59, pp. 2996-3004, 2010.
  • [16] P. K. Sahu, S. S. Ray, “Legendre spectral collocation method for Fredholm integro-differential difference equation with variable coefficients and mixed conditions,” Applied Mathematics and Computation, vol. 268, pp. 575-580, 2015.
  • [17] S. Yuzbasi, “Laguerre approach for solving pantograph-type Volterra integro-differential equations,” Applied Mathematics and Computation, vol. 232, pp. 1183–1199, 2014.
  • [18] J.K. Zhou, Differential Transformation and Its Application for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986).
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Mustafa Tolga Yavuz 0000-0001-7728-3713

İbrahim Ozkol 0000-0002-9300-9092

Yayımlanma Tarihi 1 Mayıs 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 18 Sayı: 1

Kaynak Göster

APA Yavuz, M. T., & Ozkol, İ. (2021). Solution of Integro-Differential Difference equations via Differential Transform Method. Cankaya University Journal of Science and Engineering, 18(1), 33-46.
AMA Yavuz MT, Ozkol İ. Solution of Integro-Differential Difference equations via Differential Transform Method. CUJSE. Mayıs 2021;18(1):33-46.
Chicago Yavuz, Mustafa Tolga, ve İbrahim Ozkol. “Solution of Integro-Differential Difference Equations via Differential Transform Method”. Cankaya University Journal of Science and Engineering 18, sy. 1 (Mayıs 2021): 33-46.
EndNote Yavuz MT, Ozkol İ (01 Mayıs 2021) Solution of Integro-Differential Difference equations via Differential Transform Method. Cankaya University Journal of Science and Engineering 18 1 33–46.
IEEE M. T. Yavuz ve İ. Ozkol, “Solution of Integro-Differential Difference equations via Differential Transform Method”, CUJSE, c. 18, sy. 1, ss. 33–46, 2021.
ISNAD Yavuz, Mustafa Tolga - Ozkol, İbrahim. “Solution of Integro-Differential Difference Equations via Differential Transform Method”. Cankaya University Journal of Science and Engineering 18/1 (Mayıs 2021), 33-46.
JAMA Yavuz MT, Ozkol İ. Solution of Integro-Differential Difference equations via Differential Transform Method. CUJSE. 2021;18:33–46.
MLA Yavuz, Mustafa Tolga ve İbrahim Ozkol. “Solution of Integro-Differential Difference Equations via Differential Transform Method”. Cankaya University Journal of Science and Engineering, c. 18, sy. 1, 2021, ss. 33-46.
Vancouver Yavuz MT, Ozkol İ. Solution of Integro-Differential Difference equations via Differential Transform Method. CUJSE. 2021;18(1):33-46.