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• W4288045690 abstract "Implicit block methods for solving initial value problems in ordinary differential equations are well-known among the contemporary scientific community, since they are cost-effective, self-starting, consistent, stable, and usually converge fast when applied to solve particularly stiff models. These characteristics of block methods are the primary reasons for the one-step optimized block method devised in the present research study with three off-grid points. Theoretical analysis, including the order of convergence, consistency, zero-stability, A-stability, order stars, and the local truncation error, are considered. The obtained method may be categorized as the well-known Lobatto IIIA Runge–Kutta method. The superiority of the devised method over various existing approaches having similar features is proved via numerical simulations of stiff and nonlinear differential systems. Furthermore, a suitable reformulation of the devised method results in considerable savings in computation time, as revealed through the efficiency plots. This turns out in a strategy to reformulate Runge–Kutta type methods in order to get a better performance." @default.
• W4288045690 created "2022-07-27" @default.
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• W4288045690 date "2022-09-01" @default.
• W4288045690 modified "2023-09-30" @default.
• W4288045690 title "Time-efficient reformulation of the Lobatto III family of order eight" @default.
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• W4288045690 doi "https://doi.org/10.1016/j.jocs.2022.101792" @default.
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