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A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations
Department of Mathematics, Nigerian Defence Academy, Kaduna, Nigeria
- 1 Department of Mathematics, Nigerian Defence Academy, Kaduna, Nigeria
American Journal of Computational Mathematics·Volume 04 (2014)·Pages 376–386·Published 29 August 2014·DOI10.4236/ajcm.2014.44032
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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.
KeywordsUniform OrderSecond Order Initial Value ProblemImplicit Block AlgorithmsZero Stable
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