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

Year 2022, , 184 - 190, 30.06.2022
https://doi.org/10.47000/tjmcs.1014224

Abstract

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.

Supporting Institution

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Project Number

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Thanks

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References

  • 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.
Year 2022, , 184 - 190, 30.06.2022
https://doi.org/10.47000/tjmcs.1014224

Abstract

Project Number

NA

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Pramod Pandey 0000-0003-0806-6605

Project Number NA
Publication Date June 30, 2022
Published in Issue Year 2022

Cite

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. June 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, no. 1 (June 2022): 184-90. https://doi.org/10.47000/tjmcs.1014224.
EndNote Pandey P (June 1, 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, vol. 14, no. 1, pp. 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 (June 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, vol. 14, no. 1, 2022, pp. 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.