Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, , 757 - 774, 30.12.2022
https://doi.org/10.18185/erzifbed.1009661

Öz

Destekleyen Kurum

YOK

Proje Numarası

YOK

Teşekkür

YOK

Kaynakça

  • [1] Berkovic, L.M. 1966. ‘‘The Reduction of Linear Ordinary Differential Equations to Equations with Constant Coefficients’’, Volz.Mat. Sb.5, 38-44.
  • [2] Boffa, V., Bollanti, S., Dattoli, G and Torre, A. 1983. ‘‘Second-Order Differential Equations with Variable Coefficients: Analytical Solutions’’, IL NUOVO CIMENTO, 99(1), 53-60.
  • [3] Breuer, S and Gottlieb, D. 1970. ‘‘The Reduction of Linear Ordinary Differential Equations to Equations with Constant Coefficients’’, Journal of Mathematical Analysis and Applications, 32, 62-76.
  • [4] Al-Hwawcha, L. K. and Abid, N.A. 2008. ‘‘A New Approach for Solving Second Order Ordinary Differential Equations’’, Journal of Mathematics and Statistics,4(1), 58-59.
  • [5] Munasinghe, R.2004. ‘‘Some Linear Differential Equations Forget That They Have Variable Coefficients’’, The College Mathematics Journal, 35(1), 22-25, DOI:10.1080/07468342.2004.11922046.
  • [6] Saravi, M. 2012. ‘‘A Procedure for Solving Some Second Order Linear Ordinary Differential Equations’’, Applied Mathematics Letters, 25, 408-411.
  • [7] Takayama, Ken.1986. ‘‘A Class of Solvable Second-Order Ordinary Differential Equations with Variable Coefficients’’, Journal of Mathematical Physics, 27(7), DOI: 10.1063-1.527038, 1747-1749.
  • [8] Urdaletova, A.B. and Kydyraliev, S.K. 1996. ‘‘Solving Linear Differential Equations by Operator Factorization’’, The College Mathematics Journal, 27(3), 199-203.
  • [9] Robin, W. 2007. ‘‘Operator factorization and the Solution of Second Order Linear Ordinary Differential Equations’’, Int. Journal of Mathematical Education in Science and Technology, 38(2), 189-211, DOI: 10.1080/00207390601002815.
  • [10] Wilmer III, A. and Costa, G.B.2008. ‘‘Solving Second Order Differential Equations with Variable Coefficients’’, Int. Journal of Mathematical Education in Science and Technology,39(2), 238-243, DOI: 10.1080/00207390701464709.
  • [11] Zraiqat, A. and Al-Hwawcha, L. K. 2015. ‘‘On Exact Solutions of Second Order Nonlinear Ordinary Differential Equations’’, Applied mathematics, 6, 953-957.
  • [12] Allen, J.L and Stein, F.M. 1964. ‘‘On Solutions of Certain Riccati Differential Equations’’, The American Math. Monthly, U.S.A., 1113-1115.
  • [13] Pala, Y. (2013). ‘‘Modern Uygulamalı Diferensiyel Denklemler (In Turkish)’’, Nobel Publications, Ankara, ISBN: 978-605-133-654-1, 63-69.
  • [14] Rao,P.R.P and Ukidave, V.H.1968. ‘‘Some Separable forms of the Riccati Equation’’, The American Mathematical Monthly, Vol.75, U.S.A.,38-39.
  • [15] Siller, H. 1970. ‘‘On the Separability of the Riccati Differential Equation’’, Mathematics Magazine, 43(4), U.S.A., 197-202.
  • [16] Pala, Y and Ertas, M.O. 2017. "A New Analytical Method for Solving General Riccati Equation," Universal Journal of Applied Mathematics, 5(2), 11-16, DOI: 10.13189/ujam.2017.050201.

New Analytical Method For Solution of Second Order Ordinary Differential Equations With Variable Coefficients

Yıl 2022, , 757 - 774, 30.12.2022
https://doi.org/10.18185/erzifbed.1009661

Öz

In this study, we propose four methods for the analytical solution of second order ordinary non-homogeneous differential equations with variable coefficients. In the first case, the method directly gives the solution in explicit or integral form. In the second method, the solution of the problem reduces to the solutions of adjoined second order ordinary differential equation of homogeneous type. As long as the analytical solution of two adjoined equations can be solved, the analytical solution can always be found. In the third method, the differential equation is transformed into Riccati equation. Riccati equation is solved by means of a method recently developed. In order to solve non-homogeneous differential equation, the fourth method is developed. The strategy is different but the solution is again based on the solution of Riccati equation.

Proje Numarası

YOK

Kaynakça

  • [1] Berkovic, L.M. 1966. ‘‘The Reduction of Linear Ordinary Differential Equations to Equations with Constant Coefficients’’, Volz.Mat. Sb.5, 38-44.
  • [2] Boffa, V., Bollanti, S., Dattoli, G and Torre, A. 1983. ‘‘Second-Order Differential Equations with Variable Coefficients: Analytical Solutions’’, IL NUOVO CIMENTO, 99(1), 53-60.
  • [3] Breuer, S and Gottlieb, D. 1970. ‘‘The Reduction of Linear Ordinary Differential Equations to Equations with Constant Coefficients’’, Journal of Mathematical Analysis and Applications, 32, 62-76.
  • [4] Al-Hwawcha, L. K. and Abid, N.A. 2008. ‘‘A New Approach for Solving Second Order Ordinary Differential Equations’’, Journal of Mathematics and Statistics,4(1), 58-59.
  • [5] Munasinghe, R.2004. ‘‘Some Linear Differential Equations Forget That They Have Variable Coefficients’’, The College Mathematics Journal, 35(1), 22-25, DOI:10.1080/07468342.2004.11922046.
  • [6] Saravi, M. 2012. ‘‘A Procedure for Solving Some Second Order Linear Ordinary Differential Equations’’, Applied Mathematics Letters, 25, 408-411.
  • [7] Takayama, Ken.1986. ‘‘A Class of Solvable Second-Order Ordinary Differential Equations with Variable Coefficients’’, Journal of Mathematical Physics, 27(7), DOI: 10.1063-1.527038, 1747-1749.
  • [8] Urdaletova, A.B. and Kydyraliev, S.K. 1996. ‘‘Solving Linear Differential Equations by Operator Factorization’’, The College Mathematics Journal, 27(3), 199-203.
  • [9] Robin, W. 2007. ‘‘Operator factorization and the Solution of Second Order Linear Ordinary Differential Equations’’, Int. Journal of Mathematical Education in Science and Technology, 38(2), 189-211, DOI: 10.1080/00207390601002815.
  • [10] Wilmer III, A. and Costa, G.B.2008. ‘‘Solving Second Order Differential Equations with Variable Coefficients’’, Int. Journal of Mathematical Education in Science and Technology,39(2), 238-243, DOI: 10.1080/00207390701464709.
  • [11] Zraiqat, A. and Al-Hwawcha, L. K. 2015. ‘‘On Exact Solutions of Second Order Nonlinear Ordinary Differential Equations’’, Applied mathematics, 6, 953-957.
  • [12] Allen, J.L and Stein, F.M. 1964. ‘‘On Solutions of Certain Riccati Differential Equations’’, The American Math. Monthly, U.S.A., 1113-1115.
  • [13] Pala, Y. (2013). ‘‘Modern Uygulamalı Diferensiyel Denklemler (In Turkish)’’, Nobel Publications, Ankara, ISBN: 978-605-133-654-1, 63-69.
  • [14] Rao,P.R.P and Ukidave, V.H.1968. ‘‘Some Separable forms of the Riccati Equation’’, The American Mathematical Monthly, Vol.75, U.S.A.,38-39.
  • [15] Siller, H. 1970. ‘‘On the Separability of the Riccati Differential Equation’’, Mathematics Magazine, 43(4), U.S.A., 197-202.
  • [16] Pala, Y and Ertas, M.O. 2017. "A New Analytical Method for Solving General Riccati Equation," Universal Journal of Applied Mathematics, 5(2), 11-16, DOI: 10.13189/ujam.2017.050201.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Yaşar Pala 0000-0003-0358-1958

Çağlar Kahya 0000-0002-0722-7094

Proje Numarası YOK
Yayımlanma Tarihi 30 Aralık 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Pala, Y., & Kahya, Ç. (2022). New Analytical Method For Solution of Second Order Ordinary Differential Equations With Variable Coefficients. Erzincan University Journal of Science and Technology, 15(3), 757-774. https://doi.org/10.18185/erzifbed.1009661