FOUR STEPS IMPLICIT METHOD FOR THE SOLUTION OF GENERAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
Keywords:
collocation, interpolation, continuous, implicit, Newton’s polynomial, corrector.
Abstract
Four steps implicit scheme for the solution of second order ordinary differential equation was derived through interpolation and collocation method. Newton polynomial approximation method was used to generate the unknown parameters in the corrector. The method was tested with numerical examples and it was found to be efficient in solving second order ordinary differential equations.
References
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Awoyemi, D.O., Adesanya, A.O., Ogunyebi, S.N. 2009. Construction of self Starting Numerov method for the solution of initial value problems of general second order ordinary differential equation. Int. j. Num. Math, University of Ado Ekiti,
4(2): 269-278
Milne, W.E. 1953. Numerical solution of differential equation, Wiley, New York.
Omar, Z. 1999. Developing parallel block method for solving higher orders ODES directly. Thesis, University putra Malaysia
Rosser, J.B. 1967. A Runge Kutta for all season, SIAM, P. 417-452.
Sham pine, L.F., Watts, H. 1969. Block implicit one step method, international journal of Math-comp 23: 731-740.
Worland, P.B. 1976. Parallel method for the numerical solution of ordinary differential equation, IEEE trans. Computer C-25: 1045-1048.
Yahaya, Y. A., 2007. A note on the construction of Numerov method through a quadratic continuous polynomial for the general second order ordinary differential equation. Journal of Nigerian Association of mathematical physics, II: 253-260
Zanariah Abdul, Mohamed Bin, Zurni Omar 2006. 3 point implicit block method for solving ordinary differential equation. Bulletin of the Malaysian Mathematical Science 2, 29(1):23-31
Awoyemi, D.O., Adesanya, A.O., Ogunyebi, S.N. 2009. Construction of self Starting Numerov method for the solution of initial value problems of general second order ordinary differential equation. Int. j. Num. Math, University of Ado Ekiti,
4(2): 269-278
Milne, W.E. 1953. Numerical solution of differential equation, Wiley, New York.
Omar, Z. 1999. Developing parallel block method for solving higher orders ODES directly. Thesis, University putra Malaysia
Rosser, J.B. 1967. A Runge Kutta for all season, SIAM, P. 417-452.
Sham pine, L.F., Watts, H. 1969. Block implicit one step method, international journal of Math-comp 23: 731-740.
Worland, P.B. 1976. Parallel method for the numerical solution of ordinary differential equation, IEEE trans. Computer C-25: 1045-1048.
Yahaya, Y. A., 2007. A note on the construction of Numerov method through a quadratic continuous polynomial for the general second order ordinary differential equation. Journal of Nigerian Association of mathematical physics, II: 253-260
Zanariah Abdul, Mohamed Bin, Zurni Omar 2006. 3 point implicit block method for solving ordinary differential equation. Bulletin of the Malaysian Mathematical Science 2, 29(1):23-31
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