IJSTR

International Journal of Scientific & Technology Research

IJSTR@Facebook IJSTR@Twitter IJSTR@Linkedin
Home About Us Scope Editorial Board Blog/Latest News Contact Us
CALL FOR PAPERS
AUTHORS
DOWNLOADS
CONTACT
QR CODE
IJSTR-QR Code

IJSTR >> Volume 1 - Issue 9, October 2012 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



On The Error Analysis of The New Formulation of One Step Method Into Linear Multi Step Method For The Solution of Ordinary Differential Equations

[Full Text]

 

AUTHOR(S)

Fadugba S. Emmanuel Okunlola J. Temitayo

 

KEYWORDS

Keywords: Convergence, Error, Linear Multistep Method, One Step Method, Runge Kutta Method, Zero Stability

 

ABSTRACT

Abstract-This paper presents error analysis of the new formulation of one step method into linear multistep method for the solution of ordinary differential equations. Error analysis in one step method is considerably more difficult than linear multistep method due to the loss of linearity in the method, especially for Runge Kutta Method that makes no mention of the function which defines the differential equation, makes it impossible to define the order of the method, independently of the differential equation. The new formulation of one step method into linear multistep method helps us in overcoming the shortcoming of the method. The error constant, zero stability, consistency and convergence of one step method were determined, through a similar process like linear multistep methods.

 

REFERENCES

[1] Z. A Adegboye and Y. A. Yahaya, Reformulation of Runge Kutta Method into Linear Multistep Method for Error and Convergence Analysis, Pacific Journal of Science and Technology, 13(2012), pp. 238-243.

[2] J. C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley and Sons, New York, NY, 2003.

[3] G. Dahiquist, Convergence and Stability in the Numerical Integration of Ordinary Differential Equations, Bill, 18(1956), pp. 133-136

[4] S. E. Fadugba, R. B. Ogunrinde and J. T. Okunlola, On Some Numerical Methods for Solving Initial Value Problems in Ordinary Differential Equations, International Organization of Scientific Research, Journal of Mathematics, India, 3(2012), pp. 25-31.

[5] J. D. Lambert, Computational Methods in Ordinary differential Equations, John Wiley and Sons, New York, N.Y, 1973.

[6] J. D. Lambert, Numerical Methods for Ordinary differential Equations, John Wiley and Sons, New York, N.Y, 1991.

[7] G. Yu. Kulikov, Symmetric Runge Kutta Method and their Stability, Russ J. Numeric Analyze and Maths. Modelling, 18(2003), pp. 13-41.