3-Point Block Methods for Direct Integration of General Second-Order Ordinary Differential Equations | Zendy

Julius O. Ehigie | Zendy; S. A. Okunuga | Zendy; A. B. Sofoluwe | Zendy

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3-Point Block Methods for Direct Integration of General Second-Order Ordinary Differential Equations

Author(s) -

Julius O. Ehigie,

S. A. Okunuga,

A. B. Sofoluwe

Publication year - 2011

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2011/513148

Subject(s) - block (permutation group theory) , mathematics , ordinary differential equation , linear multistep method , collocation (remote sensing) , convergence (economics) , stability (learning theory) , numerical methods for ordinary differential equations , collocation method , point (geometry) , explicit and implicit methods , differential equation , mathematical analysis , differential algebraic equation , computer science , geometry , machine learning , economic growth , economics

A Multistep collocation techniques is used in this paper to develop a 3-point explicit and implicit block methods, which are suitable for generating solutions of the general second-order ordinary differential equations of the form =(,,),(0)=,(0)=. The derivation of both explicit and implicit block schemes is given for the purpose of comparison of results. The Stability and Convergence of the individual methods of the block schemes are investigated, and the methods are found to be 0-stable with good region of absolute stability. The 3-point block schemes derived are tested on standard mechanical problems, and it is shown that the implicit block methods are superior to the explicit ones in terms of accuracy

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