Polynomial Paradigms
Description
Polynomials play an important role in developing numerical and analytical methods to solve various practical problems of physics, mathematics, engineering and industry. Problems arising in engineering and science are mathematically constructed with a variety of differential, integral and other algebraic equations. Moreover, special polynomials provide a new way to solve and investigate various equations often encountered in different practical problems. This area of research has received an ever-increasing attention and has gained a growing momentum in modern topics, such as computational probability, numerical analysis, computational wave, fluid and structural dynamics, data assimilation, statistics, image and signal processing, and artificial intelligence.
This research and reference text reports and reviews recent developments and applications of different polynomials in numerical and analytical/semi-analytical methods for solving a variety of science and engineering problems. It contains contributions from leading experts in areas such as basic theory and concepts of polynomials, mathematical modelling, mathematical physics, engineering, high-order numerical methods for differential, integral and integro-differential equations, artificial intelligence, fuzzy and interval based models and beyond. This book would be useful for graduates and researchers of various sciences and engineering fields.
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Prof. S. Chakraverty has 30 years of experience as a researcher and teacher. Presently, he is a Senior Professor at the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha. He has authored/co-authored 30 books and published 418 research papers in journals and conferences. He is on the editorial boards of various international journals, including the IOP journal Engineering Research Express. He received the IOPP Top Cited Paper Awards 2021 and 2022 for most cited articles from India, published across the IOP materials journal portfolio in the past three years respectively (2018 to 2020 and 2019 to 2021).
Content
Preface
Acknowledgement
Editor biography
List of contributors
1 Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero
2 Polynomials for meshless methods in finding solutions in gradient elasticity problems
3 Numerical solution of fractal-fractional variable orders differential equations using two-step and three-step Newton and Lagrange interpolation polynomials
4 Polynomial-based numerical methods for singularly perturbed differential equation on layer-adapted meshes
5 Modelling the impact of preventive and treatment-based control interventions on the transmission dynamics of Leptospirosis disease
6 Polynomials based semi-analytical methods for the solutions of fractional order Volterra-Fredholm integro differential equations
7 Comparing different polynomials-based shape functions in the Rayleigh-Ritz method for investigating dynamical characteristics of nanobeam
8 Application of polynomial functions in analyzing anti-plane wave profiles in a functionally graded piezoelectric-viscoelastic-poroelastic structure with buffer layer
9 Vibration analysis of single-link robotic manipulator by polynomial based Galerkin method in uncertain environment
10 Solving Type-2 Fuzzy Differential Equations Using Collocation Method with Type-2 Fuzzy Polynomials
11 Shannon entropy determination for the elastic Euler-Bernoulli beam via random polynomials and stochastic finite difference method
12 Polynomials in hybrid artificial intelligence
13 Comparative study of Chebyshev and Legendre polynomial-based neural models for approximating multidimensional poverty for an Indian State
14 Polynomial based model for solving unconstrained optimization problem with smoothing parameters
15 Interval root finding and interval polynomials: methods and applications in science and engineering
