On the Computation of First-Order Differential Systems using Refined Partitioning Algorithm
DOI:
https://doi.org/10.62054/ijdm/0301.02Abstract
In this study, a Refined Partitioning Algorithm (RPA) is formulated for the computation of differential systems of first-order. The algorithm is composed of two sub-algorithms namely the Block Hybrid Adams Algorithm (BHAA) and Block Backward Differentiation Hybrid Algorithm (BBDHA) formulated using integration and differentiation techniques respectively. In computing the solutions of a first-order differential system, the RPA initially treats the systems as non-stiff and computes it solutions using BHAA. However, if as a result of stiffness, a failure step is encountered, then the RPA automatically switches to BBDHA in order to handle the stiffness of such systems. Analyses of basic properties of the sub-algorithms that made up the RPA were established. Furthermore, the results obtained showed that the RPA is more accurate and efficient than some existing methods.
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