Volume 8, Issue 1, September 2014, Pages 195–203
Mahtab Uddin1
1 Institute of Natural Sciences, United International University, Bangladesh
Original language: English
Copyright © 2014 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is mainly analytical and comparative. Here I have proposed three new forms of predictor-corrector formulae for solving ordinary differential equation of first order and first degree. These predictor-corrector formulae have derived by taking the general forms of predictor-corrector. These formulae approximate the value of dependent variable based on five initial value of independent variable by predictor formula and then improve that initial crude value of dependent variable by corrector formula. A comparative analysis among proposed three predictor-corrector formula with Milne's predictor-corrector formula and Adam-Moulton's predictor-corrector formula by means of comparing with exact value of dependent variable have expressed as relative error. Finally, conclusive discussions have narrated.
Author Keywords: ODE, predictor-corrector formula, general form, particular form, comparative analysis, relative error, accuracy.
Mahtab Uddin1
1 Institute of Natural Sciences, United International University, Bangladesh
Original language: English
Copyright © 2014 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper is mainly analytical and comparative. Here I have proposed three new forms of predictor-corrector formulae for solving ordinary differential equation of first order and first degree. These predictor-corrector formulae have derived by taking the general forms of predictor-corrector. These formulae approximate the value of dependent variable based on five initial value of independent variable by predictor formula and then improve that initial crude value of dependent variable by corrector formula. A comparative analysis among proposed three predictor-corrector formula with Milne's predictor-corrector formula and Adam-Moulton's predictor-corrector formula by means of comparing with exact value of dependent variable have expressed as relative error. Finally, conclusive discussions have narrated.
Author Keywords: ODE, predictor-corrector formula, general form, particular form, comparative analysis, relative error, accuracy.
How to Cite this Article
Mahtab Uddin, “Five Point Predictor-Corrector Formulae and Their Comparative Analysis,” International Journal of Innovation and Applied Studies, vol. 8, no. 1, pp. 195–203, September 2014.
