Numerical Methods and Their Comparisons
Research gap analysis derived from 2 biology papers in our local library.
The gap
There is a need to compare proposed numerical methods (Adams-Bashforth scheme, Runge-Kutta methods) across different models (fractional-order chaotic systems, nonlinear transport problems) in terms of computational cost, accuracy, and stability.
Consensus across the literature
The papers collectively establish the development of new numerical schemes but leave open their comparative analysis with existing methods.
Research trend
Emerging — attention growing, methods still coalescing.
Supporting evidence — 2 representative gaps
- Adams-Bashforth Scheme and Kayo-Kengne-Akgül Derivative: Connexion and Chaotic Modelling (2026) · doi
No comparison is provided between the proposed Adams-Bashforth scheme using the Kayo-Kengne-Akgül derivative and alternative numerical schemes (e.g., Runge-Kutta methods, Predictor-Corrector methods) for fractional-order chaotic systems in terms of computational cost, accuracy, and stability across the fractional order range α ∈ [0, 1].
Keywords: Adams-Bashforth Kayo-Kengne-Akgül derivative Runge-Kutta fractional-order numerical schemes comparison - A class of non-stationary ternary 4-point subdivision schemes based on iterations (2026) · doi
No numerical experiments or computational performance comparisons are provided between the proposed schemes and existing methods beyond the theoretical comparison in Table 1.
Keywords: numerical experiments computational performance comparisons provided proposed schemes existing beyond theoretical comparison
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