Numerical Approximation Methods

Effectively Construct Integral Formulations Suitable for Numerical ImplementationFinite Element and Boundary Methods in Structural Acoustics and Vibration provides a unique and in-depth presentation o

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It co

This book offers an introduction to numerical optimization methods in structural design. Employing a readily accessible and compact format, the book presents an overview of optimization methods, and e

This text deals with combinatorics, finite calculus, formal power series and generating functions, recurrence relations, symbolic calculus and approximation formulae for finite sums. There are several

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical ana

This book focuses on the approximation of nonlinear equations using iterative methods, presenting nine contributions on the construction and analysis of the methods, including convergence, efficiency,

This book presents mathematical methods and tools which are useful for physicists and engineers: response functions, Kramers–Kronig relations, Green's functions, saddle point approximation. The deriva

This book presents mathematical methods and tools which are useful for physicists and engineers: response functions, Kramers–Kronig relations, Green's functions, saddle point approximation. The deriva

Soft computing techniques are emerging as an important tool in solving design, performance and optimisation problems in electromagnetics. Soft Computing in Electromagnetics offers detailed discussion on the application of soft computing concepts in the field of metamaterial antennas, radar absorbers, transmission line characterisation and optimised radar absorbing material (RAM) and introduces implementation of soft computing tools in a relatively new area of metamaterials. The soft computing methods are used to optimise fault detection, electromagnetic propagation and path loss detection. The development of two CAD packages for design of metamaterial split ring resonators (SRR) and path-loss prediction is discussed. The concepts are explained with the help of algorithms and the corresponding software codes. Numerical examples and MATLAB codes are provided throughout the text to facilitate understanding.

This text is designed for mathematical modeling courses that teach programming with MATLABR. Many examples show how to apply a model, select a numerical method, implement computer simulations, and ass

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate studen

Brugnano and Iavernaro deal with the numerical solution of differential problems within the framework of geometric integration, a branch of numerical analysis that aims to devise numerical methods abl

This book examines the latest research results from combined multi-component and multi-scale explorations. It provides theory, considers underlying numerical methods and presents brilliant computation

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

This book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This appro

This book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This appro

This self-contained module for independent study covers the subjects most often needed by non-mathematics graduates, such as fundamental calculus, linear algebra, probability, and basic numerical meth

This book fills a gap in the literature by introducing numerical techniques to solve problems of the Fractional Calculus of Variations (FCV). In most cases, finding the analytic solution to such probl

This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functi

Effectively Construct Integral Formulations Suitable for Numerical ImplementationFinite Element and Boundary Methods in Structural Acoustics and Vibration provides a unique and in-depth presentation o

This text focuses on a variety of topics in mathematics in common usage in graduate engineering programs including vector calculus, linear and nonlinear ordinary differential equations, approximation methods, vector spaces, linear algebra, integral equations and dynamical systems. The book is designed for engineering graduate students who wonder how much of their basic mathematics will be of use in practice. Following development of the underlying analysis, the book takes students through a large number of examples that have been worked in detail. Students can choose to go through each step or to skip ahead if they so desire. After seeing all the intermediate steps, they will be in a better position to know what is expected of them when solving assignments, examination problems, and when on the job. Chapters conclude with exercises for the student that reinforce the chapter content and help connect the subject matter to a variety of engineering problems. Students have grown up with com

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral

This book covers fundamental principles and numerical methods relevant to the modeling of the injection molding process. As injection molding processing is related to rheology, mechanical and chemical

This fourth in a suite of five practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical

This book introduces numerical programming using Python and C/C++, emphasizing methods used in physics and engineering. Its helps readers develop the ability to navigate relevant algorithms, knowledge

This book uniquely presents an overview of methods for the numerical simulation of a wide range of two-phase flows, aimed at a broad readership of engineers and scientists at graduate level. Given tha

This book provides a critical review of these and offers several more appropriate approaches for overcoming numerical convergence and the location of critical failure surfaces in two-dimensional and t

The early exercise opportunity of an American option makes it challenging to price. The Numerical Solution of the American Option Pricing Problem focuses on three numerical methods that have proved us

This book demonstrates the use of polynomial approximation from the mathematical fundamentals, through algorithm development to practical applications such as aeroplane flight dynamics or biological s

The fourth edition of this successful textbook presents a comprehensive introduction to statistical and numerical methods for the evaluation of empirical and experimental data. Equal weight is given t

This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or elect

This third in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical

Computational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathematically and practically, emphasi

Mobile Robotics offers comprehensive coverage of the essentials of the field suitable for both students and practitioners. Adapted from Alonzo Kelly's graduate and undergraduate courses, the content of the book reflects current approaches to developing effective mobile robots. Professor Kelly adapts principles and techniques from the fields of mathematics, physics and numerical methods to present a consistent framework in a notation that facilitates learning and highlights relationships between topics. This text was developed specifically to be accessible to senior level undergraduates in engineering and computer science, and includes supporting exercises to reinforce the lessons of each section. Practitioners will value Kelly's perspectives on practical applications of these principles. Complex subjects are reduced to implementable algorithms extracted from real systems wherever possible, to enhance the real-world relevance of the text.

This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential

The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive nu

The parallel developments of the Finite Element Methods in the 1950’s and the engineering applications of stochastic processes in the 1940’s provided a combined numerical analysis tool for the studies

There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

This book presents topics in a single source format using unified spectral theory of computing. With developments of DNS and LES, practitioners are rediscovering waves as important in fluid flows, and capturing these numerically is central to high accuracy computing. Analysis of waves and its use in numerical methods in propagating energy at the right velocity (dispersion effects) and with right amplitude (dissipation) are essential. Most industrial codes using Reynolds-averaged Navier–Stokes equations with turbulence models cannot conceive of capturing waves. The new themes covered in this book are: • Correct error propagation analysis • Practical compact schemes and global analysis tool • Aliasing error and its alleviation • Spurious upstream propagating q-waves • Explanation of the Gibbs phenomenon • New 1D and 2D filters for LES/DNS without SGS modelling • Anisotropic skewed wave propagation • Development and analysis of dispersion relation preservation (DRP) schemes • Flow instabi