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International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 5    
Website: http://www.ijser.org
scirp IJSER >> Volume 3,Issue 5,May 2012
Some Linear Multi-step Methods for the Initial Value Problems Y" = f(x,y,y') by Perturbed Collocation
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Author(s)
Kwanamu, J. A, Odekunle, M. R
KEYWORDS
Analytical solution, Canonical polynomials, Chebyshev-tau method, Legendre-tau method, Multi-step methods, Ordinary differential equations, Perturbed collocation
ABSTRACT
Two linear multi-step schemes for the numerical solutions of initial values problems of the type Y" = f(x,y,y') by perturbed collocation using Legendre and Chebyshev polynomials as our approximating functions in tau methods of solution were developed. The schemes were found to perform very well when compared with existing known schemes and were also found to be stable. 
References
[1] O. S. Fatunla, Numerical methods for initial value problems in ordinary differential equations. New York: Academic Press.1988.

[2] F. C. Gerald, Applied numerical analysis, (Second Edition) USA: Adision Wesley Publishing Company. 1980.

[3] B. D. Gupta, Mathematical physics. Jangpura: New Delhi Publishing House. 1978.

[4] M. K.Jain, Numerical solution of differential equation. (second edition) New Delhi: Willy Eastern. 1987.

[5] E. Kreyszig, Engineering mathematics. London: John Willy and Sons. 2001.

[6] J. D. Lambert, Numerical method for ordinary differential system. The initial value problem. London: John Willey and Sons. 1991.

[7] J. O. Oladele, P. Onumanyi, & R. O. Ayeni Derivation of linear multi-step methods for the initial value problems for o.d.es by perturbed collocation. Abacus, the Journal of Mathematical Association of Nigeria, 25 (2), 370. 1997.

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