A New Method of Embedded Fourth Order with Four Stages to Study Raster CNN Simulation

A new Runge-Kutta (PK) fourth order with four stages embedded method with error control is presented in this paper for raster simulation in cellular neural network (CNN) environment. Through versatile algorithm, single layer/raster CNN array is implemented by incorporating the proposed technique. Simulation results have been obtained, and comparison has also been carried out to show the efficiency of the proposed numerical integration algorithm. The analytic expressions for local truncation error and global truncation error are derived. It is seen that the RK-embedded root mean square outperforms the RK-embedded Heronian mean and RK-embedded harmonic mean. This work was supported as a part of Technical Quality Improvement Programme (TEQIP). R. Ponalagusamy received the M. Sc. degree in applied mathematics from Madurai Kamaraj University, India in 1981. He received the Ph.D. in computational biomechanics from the Indian Institute of Technology, Bombay, India in 1986. The Environmental Research Corporation, Tokyo, Japan, awarded him a post-doctoral fellowship for two years (1987–1988) at Chuo University, Tokyo, Japan. During June, 1989 to June, 1996, he was working as a lecturer and doing research in the field of computational fluid mechanics. During July, 1996 to June, 2005, he was working as an assistant professor and doing research in the Development of Mathematical and Computer Models in the field of processing of advanced materials, namely 1) computer aided metal flow analysis in streamlined extrusion die, 2) formability, localized, and siffusion necking, 3) wrinkling tendency of sheets metals and materials, and 4) development of yield criterion for sheet metals. From July, 2005 to till date, he has been working as a professor and guiding research students in the field of development of parallel algorithm. He is also guiding research students in the fields of parallel numerical computing and digital image processing. He has been one of the regional editors in several international Journals. He is editor-inchief for International Journal of Mathematics and Engineering with Computers (IJMAEC). He received Best Teacher Award for 2007–2008 from National Institute of Technology, Tiruchirappalli, Tamilnadu, India. He has written two books on theory of engineering plasticity and engineering mathematics. He is a life member in Indian Society of Theoretical and Applied Mechanics and Indian Society of Technical Education. He is one of the members of the World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas, Nevada, USA, during 2005–2008. His research interests include computational experimentation on biofluid mechanics, plastic flow, finite element method, computer models on metal forming and powder metallurgical materials, wavelets, digital image processing, and development of parallel algorithms. Sukumar Senthilkumr received his B. Sc. degree in mathematics from Madras University, India, M. Sc., degree in mathemati