Qualification: 
Ph.D, MSc
n_sukanta@cb.amrita.edu

Dr. Sukanta Nayak currently serves as Assistant Professor (Sr. Gr) at the Department of Mathematics, Amrita School of Engineering, Coimbatore.

Publications

Publication Type: Book

Year of Publication Title

2020

Sukanta Nayak, Fundamentals of Optimization Techniques with Algorithms (1st edition). Academic Press, ISBN: 9780128211267, 2020.[Abstract]


Optimization is a key concept in mathematics, computer science, and operations research, and is essential to the modeling of any system, playing an integral role in computer-aided design. Fundamentals of Optimization Techniques with Algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and MATLAB© code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced optimization techniques. It presents both theoretical and numerical perspectives in a clear and approachable way. In order to help the reader apply optimization techniques in practice, the book details program codes and computer-aided designs in relation to real-world problems. Ten chapters cover, an introduction to optimization; linear programming; single variable nonlinear optimization; multivariable unconstrained nonlinear optimization; multivariable constrained nonlinear optimization; geometric programming; dynamic programming; integer programming; multi-objective optimization; and nature-inspired optimization. This book provides accessible coverage of optimization techniques, and helps the reader to apply them in practice.

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2018

Sukanta Nayak and Snehashish Chakraverty, Interval Finite Element Method with MATLAB. Academic Press, 2018, p. 168.[Abstract]


Interval Finite Element Method with MATLAB provides a thorough introduction to an effective way of investigating problems involving uncertainty using computational modeling. The well-known and versatile Finite Element Method (FEM) is combined with the concept of interval uncertainties to develop the Interval Finite Element Method (IFEM). An interval or stochastic environment in parameters and variables is used in place of crisp ones to make the governing equations interval, thereby allowing modeling of the problem. The concept of interval uncertainties is systematically explained. Several examples are explored with IFEM using MATLAB on topics like spring mass, bar, truss and frame.

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Publication Type: Book Chapter

Year of Publication Title

2020

Sukanta Nayak, Tharasi Dilleswar Rao, and Snehashish Chakraverty, “Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters”, in Mathematical Methods in Interdisciplinary Sciences, John Wiley & Sons, Inc., Hoboken, New Jersey, USA., 2020, pp. 99-113.[Abstract]


Summary Diffusion plays a major role in the field of thermal and chemical engineering. It may arise in a wide range of problems, viz., heat transfer, fluid flow, and chemical diffusion. This chapter includes interval and/or fuzzy uncertainties along with well-known numerical methods, namely, finite element method and explicit finite difference method to investigate heat and gas diffusion problems. It discusses the interval and/or fuzzy finite element formulation for tapered fin and finite difference formulation for radon diffusion mechanism in uncertain environment. The chapter investigates numerical modeling of a chemical diffusion problem and a thermal diffusion problem, viz., radon diffusion mechanism with uncertain bounded parameters and triangular fuzzy number parameters.

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2020

Sukanta Nayak, “Numerical Solution of Fuzzy Stochastic Volterra-Fredholm Integral Equation with Imprecisely Defined Parameters”, in Recent Trends in Wave Mechanics and Vibrations, Springer Nature, Singapore, Snehashish Chakraverty and Biswas, P., Eds. Singapore: Springer Singapore, 2020.[Abstract]


Uncertainties play a major role in stochastic mechanics problems. To study the trajectory involved in stochastic mechanics problems generally, probability distributions are considered. Accordingly, the stochastic mechanics problems govern by stochastic differential equations followed by Markov process. However, the observation still lacks some sort of uncertainties, which are important but ignored. These imprecise uncertainties involved in the various factors affecting the constants, coefficients, initial, and boundary conditions. Hence, there may be a possibility to model a more reliable strategy that will quantify the uncertainty with better confidence. In this context, a computational method for solving fuzzy stochastic Volterra-Fredholm integral equation, which is based on the Block Pulse Functions (BPFs) using fuzzy stochastic operational matrix, is presented. The developed model is used to investigate a test problem of fuzzy stochastic Volterra integral equation and the results are compared in special cases.

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Publication Type: Journal Article

Year of Publication Title

2018

Sukanta Nayak, Tshilidzi Marwala, and S. Chakraverty, “Stochastic differential equations with imprecisely defined parameters in market analysis”, Soft Computing (Springer), vol. 23, no. 17, pp. 7715–7724, 2018.[Abstract]


Risk and uncertainties plays a major role in stock market investments. It is a pedagogical practice to deduce probability distributions for analysing stock market returns using theoretical models of investor behaviour. Generally, economists estimate probability distributions for stock market returns that are observed from the history of past returns. Besides this, there are impreciseness involved in various factors affecting market investment and returns. As such, we need to model a more reliable strategy that will quantify the uncertainty with better confidence. Here, we have presented a computational method to solve fuzzy stochastic Volterra–Fredholm integral equation which is based on the block pulse functions (BPFs) using fuzzy stochastic operational matrix (SOM). The concept of fuzziness has been hybridized with BPFs, and the corresponding stochastic integral equation has been modelled. For illustration, the developed model has been used to investigate an example problem of Black–Scholes fuzzy stochastic differential equation (FSDE), and the results are compared in special cases.

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2018

Sukanta Nayak and Snehashish Chakraverty, “Non-probabilistic solution of moving plate problem with uncertain parameters”, Journal of Fuzzy Set Valued Analysis, vol. 2018 , no. 2, pp. 49-59, 2018.[Abstract]


This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial
conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are
handled through a recently developed limit method. Here, the concepts of fuzzy numbers are combined with
Finite Difference Method (FDM) and then Fuzzy Finite Difference Method (FFDM) has been proposed. The
proposed FFDM has been used to solve the fluid flow problem bounded by two parallel plates. Finally,
sensitivity of uncertain parameters is analyzed.

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Faculty Research Interest: