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An Implicit Rational Method for Solution of Second Order Initial Value Problems in Ordinary Differential Equations

by P. K. Pandey
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 57 - Number 2
Year of Publication: 2012
Authors: P. K. Pandey
10.5120/9088-2847

P. K. Pandey . An Implicit Rational Method for Solution of Second Order Initial Value Problems in Ordinary Differential Equations. International Journal of Computer Applications. 57, 2 ( November 2012), 30-33. DOI=10.5120/9088-2847

@article{ 10.5120/9088-2847,
author = { P. K. Pandey },
title = { An Implicit Rational Method for Solution of Second Order Initial Value Problems in Ordinary Differential Equations },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 57 },
number = { 2 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 30-33 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume57/number2/9088-2847/ },
doi = { 10.5120/9088-2847 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:59:25.949448+05:30
%A P. K. Pandey
%T An Implicit Rational Method for Solution of Second Order Initial Value Problems in Ordinary Differential Equations
%J International Journal of Computer Applications
%@ 0975-8887
%V 57
%N 2
%P 30-33
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this article, we report an implicit rational method for solution of second order initial value problems in ordinary differential equation. We have presented local truncation error and stability property for the proposed method. We observed that the method has cubic rate of convergenceandA-stable. Numerical results for linear and nonlinear problems presented. These results confirm the accuracy, efficiency and effectiveness of the rational method.

References
  1. Hairer, E. ,1976 . "Methods de Nystrom pourI'equationdifferentille ",Numer. Math. 27,no. 3,283-300 .
  2. Chawla, M. M. and Sharma , S. R. ,1980 . "Families of Direct Fourth Order Methods for the Numerical Solution of General Second Order Initial Value Problems ",
  3. ZAMM 60, no. 10,469-478.
  4. Gear ,C. W. ,1971. "Numerical Initial Value Problems in Ordinary Differential Equations ", Prentice Hall.
  5. Keller, H. B. ,1968. "Numerical Methods for Two Point Boundary Value Problems ", BlaisdellWaltham Mass.
  6. Keller, H. B. ,1976. "Numerical Solution of Two Point Boundary Value Problems ", SIAM.
  7. Stoer, J. and Bulirsch , R. ,1991. "Introduction to Numerical Analysis (2/e) ", Springer-Verlag , Berlin Heidelberg .
  8. Baxley , J. V. ,1981. "Nonlinear Two Point Boundary Value Problems in Ordinary andPartial Differential Equations (Everrit , W. N. and Sleeman , B. D. Eds. ) ", 46-54 , Springer-Verlag , New York .
  9. Lambert , J. D. and Shaw , B. ,1965. "On the numerical solution of by class of formulae based on rational approximation ", Math. Comp. 19, 456-462 .
  10. Ramos , H. ,2007. "A nonstandard explicit integration scheme for initial value problems ", Applied Mathematics and Computation ,189, no. 1,710-718 .
  11. Okosun , K. O. and Ademiluyi , R. A. ,2007. "A Three Step Rational Methods forIntegration of Differential Equations with Singularities", Research Journal of Applied Sciences ,2(1),84-88 .
  12. Lambert , J. D. ,1991. "Numerical Methods for Ordinary Differential systems ", John Wiley , England .
  13. VanNiekerk, F. D. ,1987. "Nonlnear one-step methods for initial value problems",Comput. Math. Appl. , 13, 367-371.
  14. Dahlquist , G. ,1963. "A special stability problem for linear multistep methods ", BIT,3, 27-43 .
  15. Jain , M. K. , Iyenger , S. R. K. and Jain , R. K. ,1987 . "Numerical Methods for Scientificand Engineering Computation (2/e)", Wiley Eastern Ltd. New Delhi .
  16. Bulatov , M. V. and Berghe , G. V. , 2009 . "Two Step Fourth Order Methods for LinearODEs of the Second Order ", Numer. Algor. 51, 449-460 .
Index Terms

Computer Science
Information Sciences

Keywords

Implicit method Rational method Non-standard method Initial value problems Ordinary differential equations Cubic order convergence

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