Keywords:-

Keywords: Exponentially Fitted Collocation Method (EFCM), homogeneous equations, Initial value problems (IVP), rate of convergence, analytical and numerical solutions

Article Content:-

Abstract

The Exponentially Fitted Method (EFM) is an analytical and numerical method for solving various homogeneous equations. In this study,we proposed a reliable numerical method named Exponentially Fitted Collocation Method (EFCM) which will increase the rate of convergence of the initial value problems. The new method is applied to third order homogenous initial value problems. The comparative study between exact solution and Exponentially Fitted Collocation Method (EFCM) is presented. The results demonstrate liability and efficiency of the new method developed.

References:-

References

Morton M. and Joseph W. “Introduction to General Physics”second edition pp229-245 (1938)

Wilson B. “College Physics” Fouth edition prentice Hall inc.Upper saddle river new Jersey pp142-147 (2000)

Jeffrey R. “Introduction to Differential Equations” Lecture note for MTH2351/2352 pp31-37 (2009)

Taiwo O. A. “Exponential Fitting for the Solution of Two Point Boundary Value Problems (BVP) with Cubic Spline Collocated Tau Method”. International Journal Computer Mathematics pp 1 – 8 (2002)

Adejide and Adenira “A five-step ninth order hybrid linear multi-step method for the solution of the first order initial value problem via the interpolation and collocation procedure”Internation.Journal of Applied Mathematics .Vol.12 pp314-334 (2002) .

Yang C. and Guo.B “A collocation Method for Initial Value Problems of Second-Order ODEs by using Languarre Functions”. Numerical Mathematics Theory Method Application Vol. 4 No 2 pp 283 – 395. (2011).

Fox, L. “Chebyshev methods for Ordinary Differential equations”,

Computer J. 4, pp318 – 331 (1962):

Lanczos, C. “Table of Chebyshev Polynomials” National Bureau

of standards, Appl. Maths Series, 9 Washington: Gov Printing office. (1952)

Miller, J.C.P. “Two numerical approximation of Chebyshev Polynomials”, Proc. Rey. Soc. Edinb. Lxii, pp. 204 – 210 (1946).

Onumanyi, P, Oladele, J.O, Adeniyi, R.B and Awoniyi, D.O,“Derivation of finite differences methods by Collocation”, Abacus Vol. 23.No.2 pp.76-83 , (1993):.

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Taiwo, O., Falade, K., & Rafiu, S. (2014). Numerical Solution of Third Order Homogenous Differential Equations Using Exponentially Fitted Collocation Method (EFCM). International Journal Of Mathematics And Computer Research, 2(09), 639-653. Retrieved from http://ijmcr.in/index.php/ijmcr/article/view/171