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Investigation on Non-Standard Scheme Applied to Euler and Third Order Euler for Initial Value Problems

by Nurhafizah Moziyana Mohd Yusop, Mohammad Khatim Hasan, Mohd Fahmi Mohamad Amran, Muslihah Wook
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 155 - Number 14
Year of Publication: 2016
Authors: Nurhafizah Moziyana Mohd Yusop, Mohammad Khatim Hasan, Mohd Fahmi Mohamad Amran, Muslihah Wook
10.5120/ijca2016912302

Nurhafizah Moziyana Mohd Yusop, Mohammad Khatim Hasan, Mohd Fahmi Mohamad Amran, Muslihah Wook . Investigation on Non-Standard Scheme Applied to Euler and Third Order Euler for Initial Value Problems. International Journal of Computer Applications. 155, 14 ( Dec 2016), 7-10. DOI=10.5120/ijca2016912302

@article{ 10.5120/ijca2016912302,
author = { Nurhafizah Moziyana Mohd Yusop, Mohammad Khatim Hasan, Mohd Fahmi Mohamad Amran, Muslihah Wook },
title = { Investigation on Non-Standard Scheme Applied to Euler and Third Order Euler for Initial Value Problems },
journal = { International Journal of Computer Applications },
issue_date = { Dec 2016 },
volume = { 155 },
number = { 14 },
month = { Dec },
year = { 2016 },
issn = { 0975-8887 },
pages = { 7-10 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume155/number14/26772-2016912302/ },
doi = { 10.5120/ijca2016912302 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:01:13.576778+05:30
%A Nurhafizah Moziyana Mohd Yusop
%A Mohammad Khatim Hasan
%A Mohd Fahmi Mohamad Amran
%A Muslihah Wook
%T Investigation on Non-Standard Scheme Applied to Euler and Third Order Euler for Initial Value Problems
%J International Journal of Computer Applications
%@ 0975-8887
%V 155
%N 14
%P 7-10
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

There are many benefits to improve methods of Euler for solving the initial value problem (IVPs). Among the good is a simple implementation and low-cost computational. However, there are problems of accuracy and instability in the Euler method. Therefore, the main purpose of this research is to discuss the improvement of the Euler method using Non-standard Finite Difference (NSFD) scheme in the Initial Value Problems(IVPs). The study is done using a NSFD in the Euler and the Third Order Euler (TOE) method. Combinations of these methods can provide advantages such as easy implementation, low computational cost and better accuracy. Linear and nonlinear IVPs will be tested using SCILAB. About six various problems used to test with various step sizes. The result obtained shows that the NSFD approaching the exact solution.

References
  1. K. Moaddy et al., A New Hybrid Nonstandard Finite Difference Adomian Scheme for Solution of Nonlinear Equations, Sains Malaysiana, 2011, pp. 515-519.
  2. R. E. Mickens, Advances in the Application of Nonstandard Finite Differences Schemes, Singapore : World Scientific, 2005
  3. R. E. Mickens, An Introduction Finite Difference Models of Differential Equations, Journal of Computational Acoustics, 1999, pp 39-59.
  4. P. M. Manning and G. F. Margrave, Introduction to Non-standard Finite-difference Modeling, CREWES Research Report, 2006, pp 1-10.
  5. S. Fadugba, et al., Euler Method for Solving Initial Value Problems in Ordinary Differential Equations, The Pacific Journal of Science and Technology, 2012, pp 152-158.
  6. R. E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, 1994, pp 81-85.
  7. P. Kama, “Non-standard Finite Difference Methods in Dynamical Systems”, Ph.D. Thesis, University of Pretoria, 2009.
  8. A. K. Gucoglu, “The Solution of Some Differential Equations by Nonstandard Finite Difference Method”, Master Thesis, Izmir Institute of Technology, 2005.
  9. G. E. Urroz, Introduction to SCILAB, 2001, pp 1-17.
  10. Z. B. Ibrahim et al., Block Method for Generalised Multistep Adams and Backward Differentiation Formulae in Solving First Order ODEs, MATEMATIKA, 2005, pp 25-33
Index Terms

Computer Science
Information Sciences

Keywords

Non-standard Finite Difference Scheme Initial Value Problem Euler

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