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A new fourth order embedded $\text{RKAHeM}(4,4)$ method with error control on multilayer raster cellular neural network. (English) Zbl 1179.65087
Summary: We introduce a new technique for solving initial value problems (IVPs) with error control by formulating an embedded method involving Runge-Kutta (RK) methods based on arithmetic mean (AM) and Heronian mean (HeM). The function of the simulator is that it is capable of performing raster simulation for any kind as well as any size of input image. It is a powerful tool for researchers to examine the potential applications of cellular neural networks (CNN). By using the newly proposed embedded method, a versatile algorithm for simulating multilayer CNN arrays is implemented. This article proposes an efficient pseudo code for exploiting the latency properties of CNN along with well known RK-fourth order embedded numerical integration algorithms. Simulation results and comparison are also presented to show the efficiency of the numerical integration algorithms. It is found that the RK-embedded Heronian mean outperforms well in comparison with the RK-embedded centroidal mean, harmonic mean and contra-harmonic mean. A more quantitative analysis is carried out to clearly visualize the goodness and robustness of the proposed algorithm.
##### MSC:
 65L06 Multistep, Runge-Kutta, and extrapolation methods 65L05 Initial value problems for ODE (numerical methods) 65L70 Error bounds (numerical methods for ODE) 34A34 Nonlinear ODE and systems, general
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