A Class of Adams-like Implicit Collocation Methods of Higher Orders for the solutions of Initial Value Problems | Zendy

Johnson O. Fatokun | Zendy; Tsaku. Nuhu | Zendy; I. K. O. Ajibola | Zendy

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A Class of Adams-like Implicit Collocation Methods of Higher Orders for the solutions of Initial Value Problems

Author(s) -

Johnson O. Fatokun,

Tsaku. Nuhu,

I. K. O. Ajibola

Publication year - 2011

Publication title -

material science research india

Language(s) - English

Resource type - Journals

eISSN - 2394-0565

pISSN - 0973-3469

DOI - 10.13005/msri/080107

Subject(s) - linear multistep method , collocation (remote sensing) , quadrature (astronomy) , convergence (economics) , mathematics , focus (optics) , class (philosophy) , gaussian quadrature , collocation method , initial value problem , calculus (dental) , mathematical analysis , computer science , nyström method , differential equation , physics , integral equation , ordinary differential equation , optics , medicine , differential algebraic equation , dentistry , machine learning , artificial intelligence , economic growth , economics

The focus of this research work is the derivation of a class of Adams-like collocation multistep methods of orders not exceeding p=9. Numerical quadrature rule is used to derive steps k= 3,...,8 of the Adams methods. Convergence of each formula derived is established in this paper. As a numerical experiment, the step six pair of the Adams method so derived was used as predictor-corrector pair to solve a non-stiff initial value problem. The absolute errors show an accuracy of o(h7).

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