Hybrid Block Method for Direct Integration of First, Second and Third Order IVPs

Authors : Adeyemi OLAGUNJU, Emmanuel ADEYEFA

Pages : 1-8

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Publication Date : 2021-05-01

Article Type : Research Paper

Abstract :Construction of numerical methods for the solution of initial value problems insert ignore into journalissuearticles values(IVPs); in ordinary differential equations insert ignore into journalissuearticles values(ODEs); has been considered overwhelmingly in literature. However, the use of a single numerical method for the integration of ODEs of more than one order has not been commonly reported. In this paper, we focus on the development of a numerical method capable of obtaining the numerical solution of first, second and third-order IVPs. The method is formulated from continuous schemes obtained via collocation and interpolation techniques and applied in a block-by-block manner as a numerical integrator for first, second and third-order ODEs. The convergence properties of the method are discussed via zero-stability and consistency. Numerical examples are included and comparisons are made with existing methods in the literature.
Keywords : Consistency, Convergence, Zero Stability