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This book offers an ideal introduction to singular perturbation
problems, and a valuable guide for researchers in the field of
differential equations. It also includes chapters on new
contributions to both fields: differential equations and singular
perturbation problems. Written by experts who are active
researchers in the related fields, the book serves as a
comprehensive source of information on the underlying ideas in the
construction of numerical methods to address different classes of
problems with solutions of different behaviors, which will
ultimately help researchers to design and assess numerical methods
for solving new problems. All the chapters presented in the volume
are complemented by illustrations in the form of tables and graphs.
This book offers an ideal introduction to singular perturbation
problems, and a valuable guide for researchers in the field of
differential equations. It also includes chapters on new
contributions to both fields: differential equations and singular
perturbation problems. Written by experts who are active
researchers in the related fields, the book serves as a
comprehensive source of information on the underlying ideas in the
construction of numerical methods to address different classes of
problems with solutions of different behaviors, which will
ultimately help researchers to design and assess numerical methods
for solving new problems. All the chapters presented in the volume
are complemented by illustrations in the form of tables and graphs.
Presenting state-of-the-art methods in the area, the book begins
with a presentation of weak discrete time approximations of
jump-diffusion stochastic differential equations for derivatives
pricing and risk measurement. Using a moving least squares
reconstruction, a numerical approach is then developed that allows
for the construction of arbitrage-free surfaces. Free boundary
problems are considered next, with particular focus on stochastic
impulse control problems that arise when the cost of control
includes a fixed cost, common in financial applications. The text
proceeds with the development of a fear index based on equity
option surfaces, allowing for the measurement of overall fear
levels in the market. The problem of American option pricing is
considered next, applying simulation methods combined with
regression techniques and discussing convergence properties.
Changing focus to integral transform methods, a variety of option
pricing problems are considered. The COS method is practically
applied for the pricing of options under uncertain volatility, a
method developed by the authors that relies on the dynamic
programming principle and Fourier cosine series expansions.
Efficient approximation methods are next developed for the
application of the fast Fourier transform for option pricing under
multifactor affine models with stochastic volatility and jumps.
Following this, fast and accurate pricing techniques are showcased
for the pricing of credit derivative contracts with discrete
monitoring based on the Wiener-Hopf factorisation. With an energy
theme, a recombining pentanomial lattice is developed for the
pricing of gas swing contracts under regime switching dynamics. The
book concludes with a linear and nonlinear review of the
arbitrage-free parity theory for the CDS and bond markets.
This book collects select papers presented at the International
Conference on Applications of Basic Sciences, held at
Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The
book discusses topics on singular perturbation problems,
differential equations, numerical analysis, fuzzy logics, fuzzy
differential equations, and mathematical physics, and their
interdisciplinary applications in all areas of basic sciences:
mathematics, physics, chemistry, and biology. It will be useful to
researchers and scientists in all disciplines of basic sciences.
This book will be very useful to know the different scientific
approaches for a single physical system.
Since the first edition of this book, the literature on fitted mesh
methods for singularly perturbed problems has expanded
significantly. Over the intervening years, fitted meshes have been
shown to be effective for an extensive set of singularly perturbed
partial differential equations. In the revised version of this
book, the reader will find an introduction to the basic theory
associated with fitted numerical methods for singularly perturbed
differential equations. Fitted mesh methods focus on the
appropriate distribution of the mesh points for singularly
perturbed problems. The global errors in the numerical
approximations are measured in the pointwise maximum norm. The
fitted mesh algorithm is particularly simple to implement in
practice, but the theory of why these numerical methods work is far
from simple. This book can be used as an introductory text to the
theory underpinning fitted mesh methods.
This book collects select papers presented at the International
Conference on Applications of Basic Sciences, held at
Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The
book discusses topics on singular perturbation problems,
differential equations, numerical analysis, fuzzy logics, fuzzy
differential equations, and mathematical physics, and their
interdisciplinary applications in all areas of basic sciences:
mathematics, physics, chemistry, and biology. It will be useful to
researchers and scientists in all disciplines of basic sciences.
This book will be very useful to know the different scientific
approaches for a single physical system.
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