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 AJCM  Vol.4 No.4 , September 2014
A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations
Abstract: This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
Cite this paper: Badmus, A. (2014) A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations. American Journal of Computational Mathematics, 4, 376-386. doi: 10.4236/ajcm.2014.44032.
References

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[2]   Badmus, A.M. and Ekpenyong, F.E. (2013) High Order Block Method for Direct Solution of General Second Order Ordinary Differential Equations. Academy Journal of Science and Engineering, Nigerian Defence Academy Kaduna, 7, 36-42.

[3]   Badmus, A.M. and Yahaya, Y.A. (2009) An Accurate Uniform Order 6 Block Method for Direct Solution of General Second Order Ordinary Differential Equations. The Pacific Journal of Science and Technology, 10, 248-254.

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[11]   Vigo-Angular, J. and Ramos, H. (2006) Variable Step-Size Implementation of Multi-Step Methods . Journal of Computation and Applied Mathematics, 92, 114-131.
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[13]   Yahaya, Y.A. (2004) Some Theories and Applications of Continuous LMM for Ordinary Differential Equations. PhD Thesis (Unpublished), University of Jos, Nigeria.

[14]   Badmus, A.M. and Mshelia, D.W. (2012) Uniform Order Zero Stable k-Step Block Methods for Initial Value Problems of Ordinary Differential Equations. Journal of Nigerian Association of Mathematical Physics, 20, 65-74.

[15]   Badmus, A.M. (2014) An Efficient Seven Point Block Method for Direct Solution of General Second Order Ordinary Differential Equations . British Journal of Mathematics and Computer Science, 4, 2840-2852.
http://dx.doi.org/10.9734/BJMCS/2014/6749

 
 
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