TWO STEPS BLOCK METHOD FOR THE SOLUTION OF GENERAL SECOND ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATION
Keywords:
Implicit, linear Multistep, Predictor, Corrector, Block Method.
Abstract
In this paper, an implicit block linear multistep method for the solution of ordinary differential equation was extended to the general form of differential equation. This method is self starting and does not need a predictor to solve for the unknown in the corrector. The method can also be extended to boundary value problems without additional cost. The method was found to be efficient after being tested with numerical problems of second order.
References
Aladeselu, V.A. 2007. Improved family of block method for special second order initial value problems (I.V.Ps). Journal of the Nigerian Association of Mathematical Physics, 11: 153-158.
Awoyemi, D.O. 1999. A class of Continuous Methods for general second order initial value problems in ordinary differential equation. International Journal of Computational Mathematics, 72: 29-37.
Awoyemi, D.O. 1996. An efficient two-step numerical integrator for general second order ordinary differential equation. ABACUS, Journal of Mathematical Association of Nigeria, 24(2): 31-43.
Awoyemi, D.O., Udoh, M.O., Adesanya A.O. 2006. Non-symmetric collocation method for direct solution of general third order initial value problems of ordinary differential equation journal of Natural and Applied Sciences, 7(1): 31-37
Yahaya, Y.A. 2007. A note on the construction of Numerov’s method through a quadratic continuous polynomial for the general second order differential equation. Journal of the Nigerian Association of Mathematical Physics, II, 253-260.
Awoyemi, D.O. 1999. A class of Continuous Methods for general second order initial value problems in ordinary differential equation. International Journal of Computational Mathematics, 72: 29-37.
Awoyemi, D.O. 1996. An efficient two-step numerical integrator for general second order ordinary differential equation. ABACUS, Journal of Mathematical Association of Nigeria, 24(2): 31-43.
Awoyemi, D.O., Udoh, M.O., Adesanya A.O. 2006. Non-symmetric collocation method for direct solution of general third order initial value problems of ordinary differential equation journal of Natural and Applied Sciences, 7(1): 31-37
Yahaya, Y.A. 2007. A note on the construction of Numerov’s method through a quadratic continuous polynomial for the general second order differential equation. Journal of the Nigerian Association of Mathematical Physics, II, 253-260.
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