Many important problems in engineering and science are modeled by nonlinear partial differential equations (PDEs). A new trend in PDEs, called structure-preserving numerical methods, has recently developed. This book introduces key factors and basic ideas of discrete variational derivative method.
Introduction to Computational Engineering with MATLAB(R) aims to teach readers how to use MATLAB programming to solve numerical engineering problems. The book focuses on computational engineering with the objective of helping engineering students improve their numerical problem-solving skills. The book cuts a middle path between undergraduate texts that simply focus on programming and advanced mathematical texts that skip over foundational concepts, feature cryptic mathematical expressions, and do not provide sufficient support for novices.Although this book covers some advanced topics, readers do not need prior computer programming experience or an advanced mathematical background. Instead, the focus is on learning how to leverage the computer and software environment to do the hard work. The problem areas discussed are related to data-driven engineering, statistics, linear algebra, and numerical methods. Some example problems discussed touch on robotics, control systems, and machine learning.Features:Demonstrates through algorithms and code segments how numeric problems are solved with only a few lines of MATLAB code Quickly teaches students the basics and gets them started programming interesting problems as soon as possibleNo prior computer programming experience or advanced math skills required Suitable for students at undergraduate level who have prior knowledge of college algebra, trigonometry, and are enrolled in Calculus IMATLAB script files, functions, and datasets used in examples are available for download from http://www.routledge.com/9781032221410.
Until the authors¿ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science.
Greenwich has been a centre for scientific computing since the foundation of the Royal Observatory in 1675. This book presents an account of the mathematicians who worked at Greenwich and their achievements.
Reflecting the author's advances with Sinc since 1995, this handbook contains roughly 450 MATLAB (R) programs for approximating almost every type of operation stemming from calculus. It also presents new and powerful methods for solving ordinary differential equations, partial differential equations, and integral equations. The book makes Sinc meth
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites, the text covers discrete mathematics, data structures, and computational physics, including high-order discretization of nonlinear equations. Exercises and solutions make the book suitable for classroom use and a supporting website supplies downloadable code.
This book provides efficient and reliable numerical methods for solving fractional calculus problems. It focuses on numerical techniques for fractional integrals, derivatives, and differential equations. The book covers frequently used fractional integrals and derivatives, explains how to implement fractional finite difference methods in various fractional differential equations relevant to scientific and engineering applications, and presents the finite element method for solving fractional PDEs. Many numerical examples support the theoretical analyses and MATLAB® functions are available on the book¿s CRC Press web page.
General purpose graphics processing units (GPGPUs) enable researchers in a variety of fields to benefit from the computational power of all the cores available inside graphics cards. This book shows you how to use GPUs for applications in diverse scientific fields, from physics and mathematics to computer science. The book explains the methods necessary for designing or porting your scientific application on GPUs and will improve your knowledge about image processing, numerical applications, methodology to design efficient applications, optimization methods, and much more.
Until the authors¿ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science.
Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models.
Helps in solving numerical problems in mathematics, computer science, and engineering. This book employs sinc methods by limiting details as to how or why these methods work. It is suitable to approximate various types of operation, from calculus to partial differential and integral equations.
Exploring iterative operator-splitting methods, this work describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It generalizes the numerical analysis with respect to the consistency and stability to nonlinear, stiff, and spatial decomposed splitting problems.
Provides a foundation in numerical analysis for such topics as - finite element theory, advanced numerical linear algebra, and optimization. This book covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, numerical integration, and boundary value problems.
Covers image segmentation, object recognition, and morphology. This book includes industrial practices for image compression, image de-noising methods based on partial differential equations, and fresh image compression methods such as fractal image compression and wavelet compression.
Covers basic techniques for DNS and LES that can be applied to practical problems of flow, turbulence, and combustion. This work presents numerical methods for compressible and incompressible three-dimensional flows, such as high-order discretization schemes, high-fidelity boundary conditions, and coupling aspects.
Focusing on algorithms for distributed-memory parallel architectures, this book covers theoretical models of parallel computation, parallel algorithm design for homogeneous and heterogeneous platforms, complexity and performance analysis, and essential notions of scheduling.
An overview of the next generation in computing. It explores grid projects, core grid technologies, and applications of the grid. It covers virtual organizations, scheduling algorithms, fault tolerance strategies, grid workflow management systems, and security technologies.
Helping readers numerically solve optimization problems, this book focuses on the fundamental principles and applications of PSO and QPSO algorithms. The authors develop their novel QPSO algorithm, a PSO variant motivated from quantum mechanics, and show how to implement it in real-world applications, including inverse problems, digital filter d
Helping readers numerically solve optimization problems, this book focuses on the fundamental principles and applications of PSO and QPSO algorithms. The authors develop their novel QPSO algorithm, a PSO variant motivated from quantum mechanics, and show how to implement it in real-world applications, including inverse problems, digital filter d
Greenwich has been a centre for scientific computing since the foundation of the Royal Observatory in 1675. This book presents an account of the mathematicians who worked at Greenwich and their achievements.
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