A new method of embedded fourth order with four stages to study raster CNN simulation |
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Authors: | R Ponalagusamy S Senthilkumar |
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Affiliation: | (1) Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, India |
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Abstract: | 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 mathematics from Bharathidasan
University, India in 1996, M. Phil degree in mathematics from Bharathidasan University in 1999, and M. Phil degree in computer
science and engineering from Bharathiar University in 2000. Also, he received PGDCA and PGDCH in computer applications and
computer hardware from Bharathidasan University in 1996 and 1997, respectively. He is currently a Ph.D. candidate in the Department
of Mathematics at National Institute of Technology, Tiruchirappalli, Tamilnadu, India. He served as a lecturer, in the Department
of Computer Science at Asan Memorial College of Arts and Science, Chennai, Tamilnadu, India.
His research interests include digital image processing and numerical methods. |
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Keywords: | Raster scheme cellular neural network (CNN) numerical integration techniques edge detection new embedded Runge Kutta root mean square (RKARMS (4 4)) method truncation errors |
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