Bøker av Santanu Saha Ray

The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes - either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.

This book is a compendium of the proceedings of the International Conference on Applied Analysis, Computation, and Mathematical Modelling in Engineering (AACMME-2021). The book covers a variety of applications such as mechanical, acoustical, physical, electrical, bio-mathematical, and computational fluid dynamics. Since mathematical modeling necessitates a wide range of skills and methods, the book concentrates on techniques that will be of specific interest to engineers, scientists, and those who work with discrete and continuous systems models. This book guides students, researchers, and professionals through the new approaches, the powerful tools for quickly mastering the most popular mathematical and computational models used in engineering and science. These new approaches enable readers to not only systematically create effective models, but also extend these models to any macroscopic physical structure.

This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency.

This is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. The book presents many techniques for the efficient numerical solution of problems in science and engineering. It develops students¿ understanding of the construction of numerical algorithms and the applicability of the methods. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation.

This book covers the applications of new analytical and numerical methods, including wavelet methods to explain the physical behavior of nuclear reactors. Fractional calculus represents the reactor more closely than classical integer order calculus. The reactor kinetics model has therefore been presented in this context and analytical and numerical solutions have been provided. Describing the reactor through fractional calculus helps readers understand fractional order control and achieve overall plant efficiency.