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Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs

Yıl 2022, Cilt: 14 Sayı: 1, 184 - 190, 30.06.2022
https://doi.org/10.47000/tjmcs.1014224

Öz

We propose a third order convergent finite-difference method for the approximate solution of the boundary value problems. We developed our numerical technique by employing Taylor series expansion and method of undetermined coefficients. The convergence property of the proposed finite difference method discussed. To demonstrate the computational accuracy and effectiveness of the proposed method numerical results presented.

Destekleyen Kurum

NA

Proje Numarası

NA

Teşekkür

NA

Kaynakça

  • Agarwal, R.P., Boundary Value Problems for Higher Order Differential Equations, World Scientific, Singapore, 1986.
  • Al-Said, E.A., Numerical solutions for system of third-order boundary value problems, International Journal of Computer Mathematics, 78(1)(2001), 111-121 .
  • Froberg, C.E., Introduction to Numerical Analysis, 2nd ed., Addison-Wesley, New York, 1969.
  • Gregus, M., Third Order Linear Differential Equations, Series: Mathematics and its Applications, Vol. 22., Springer Netherlands, 1987.
  • Gupta, C.P.,Lakshmikantham, V., Existence and uniqueness theorems for a third-order three point boundary value problem, Nonlinear Analysis: Theory, Methods & Applications, 16(11)(1991), 949-957.
  • Henderson, J., Thompson, H.B., Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations, J. Differential Equations Appl.,70(2)(2001), 297-321.
  • Islam, S., Khan, M.A., Tirmizi, I.A., Twizell, E.H., Non-polynomial splines approach to the solution of a system of third order boundary value problems, Applied Mathematics and Computation, 168(1)(2005), 152-163.
  • Khan, A., Aziz, T., The numerical solution of third order boundary value problems using quintic splines, Applied Mathematics and Computation, 137(2-3)(2003), 253-260.
  • Murty, K.N., Rao, Y.S., A theory for existence and uniqueness of solutions to three-point boundary value problems, Journal of Mathematical Analysis and Applications, 167(1)(1992), 43-48.
  • Pandey, P.K., An efficient numerical method for the solution of third order boundary value problem in ordinary differential equations, Int. J. Computing Science and Mathematics, 9(2)(2018), 171-180.
  • Salama, A.A., Mansour, A.A., Fourth-order finite-difference method For third-order boundary-value problems, Numerical Heat Transfer, Part B, 47(2005), 383-401.
  • Varga, R.S., Matrix Iterative Analysis, Second Revised and Expanded Edition, SpringerVerlag, Heidelberg, 2000.
  • Xie, S., Li, P., Gao, Z., Wang, H., High order compact finite difference schemes for a system of third order boundary value problem, Applied Mathematics and Computation, 219(2012), 2564-2573.
Yıl 2022, Cilt: 14 Sayı: 1, 184 - 190, 30.06.2022
https://doi.org/10.47000/tjmcs.1014224

Öz

Proje Numarası

NA

Kaynakça

  • Agarwal, R.P., Boundary Value Problems for Higher Order Differential Equations, World Scientific, Singapore, 1986.
  • Al-Said, E.A., Numerical solutions for system of third-order boundary value problems, International Journal of Computer Mathematics, 78(1)(2001), 111-121 .
  • Froberg, C.E., Introduction to Numerical Analysis, 2nd ed., Addison-Wesley, New York, 1969.
  • Gregus, M., Third Order Linear Differential Equations, Series: Mathematics and its Applications, Vol. 22., Springer Netherlands, 1987.
  • Gupta, C.P.,Lakshmikantham, V., Existence and uniqueness theorems for a third-order three point boundary value problem, Nonlinear Analysis: Theory, Methods & Applications, 16(11)(1991), 949-957.
  • Henderson, J., Thompson, H.B., Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations, J. Differential Equations Appl.,70(2)(2001), 297-321.
  • Islam, S., Khan, M.A., Tirmizi, I.A., Twizell, E.H., Non-polynomial splines approach to the solution of a system of third order boundary value problems, Applied Mathematics and Computation, 168(1)(2005), 152-163.
  • Khan, A., Aziz, T., The numerical solution of third order boundary value problems using quintic splines, Applied Mathematics and Computation, 137(2-3)(2003), 253-260.
  • Murty, K.N., Rao, Y.S., A theory for existence and uniqueness of solutions to three-point boundary value problems, Journal of Mathematical Analysis and Applications, 167(1)(1992), 43-48.
  • Pandey, P.K., An efficient numerical method for the solution of third order boundary value problem in ordinary differential equations, Int. J. Computing Science and Mathematics, 9(2)(2018), 171-180.
  • Salama, A.A., Mansour, A.A., Fourth-order finite-difference method For third-order boundary-value problems, Numerical Heat Transfer, Part B, 47(2005), 383-401.
  • Varga, R.S., Matrix Iterative Analysis, Second Revised and Expanded Edition, SpringerVerlag, Heidelberg, 2000.
  • Xie, S., Li, P., Gao, Z., Wang, H., High order compact finite difference schemes for a system of third order boundary value problem, Applied Mathematics and Computation, 219(2012), 2564-2573.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Pramod Pandey 0000-0003-0806-6605

Proje Numarası NA
Yayımlanma Tarihi 30 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 14 Sayı: 1

Kaynak Göster

APA Pandey, P. (2022). Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs. Turkish Journal of Mathematics and Computer Science, 14(1), 184-190. https://doi.org/10.47000/tjmcs.1014224
AMA Pandey P. Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs. TJMCS. Haziran 2022;14(1):184-190. doi:10.47000/tjmcs.1014224
Chicago Pandey, Pramod. “Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs”. Turkish Journal of Mathematics and Computer Science 14, sy. 1 (Haziran 2022): 184-90. https://doi.org/10.47000/tjmcs.1014224.
EndNote Pandey P (01 Haziran 2022) Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs. Turkish Journal of Mathematics and Computer Science 14 1 184–190.
IEEE P. Pandey, “Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs”, TJMCS, c. 14, sy. 1, ss. 184–190, 2022, doi: 10.47000/tjmcs.1014224.
ISNAD Pandey, Pramod. “Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs”. Turkish Journal of Mathematics and Computer Science 14/1 (Haziran 2022), 184-190. https://doi.org/10.47000/tjmcs.1014224.
JAMA Pandey P. Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs. TJMCS. 2022;14:184–190.
MLA Pandey, Pramod. “Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs”. Turkish Journal of Mathematics and Computer Science, c. 14, sy. 1, 2022, ss. 184-90, doi:10.47000/tjmcs.1014224.
Vancouver Pandey P. Third Order Convergent Finite Difference Method for the Third Order Boundary Value Problem in ODEs. TJMCS. 2022;14(1):184-90.