Numerical Approximation Methods

This book mainly focuses on MOR techniques for the first and second order descriptor systems. The book also provides mathematical algorithms for implementing them in real-world applications. This book

In the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physi

This book presents applications of Newton-like and other similar methods to solve abstract functional equations involving fractional derivatives. It focuses on Banach space-valued functions of a real

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what i

This book provides an overview of the standard topics of numerical analysis but uses R as the underlying programming language. There are many textbooks for numerical analysis, many of them using MATLA

This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based o

Designed primarily for undergraduates, but also graduates and practitioners, this textbook integrates numerical methods and programming with applications from chemical engineering. Combining mathematical rigor with an informal writing style, it thoroughly introduces the theory underlying numerical methods, its translation into MATLAB programs, and its use for solving realistic problems. Specific topics covered include accuracy, convergence and numerical stability, as well as stiffness and ill-conditioning. MATLAB codes are developed from scratch, and their implementation is explained in detail, all while assuming limited programming knowledge. All scripts employed are downloadable, and built-in MATLAB functions are discussed and contextualised. Numerous examples and homework problems - from simple questions to extended case studies - accompany the text, allowing students to develop a deep appreciation for the range of real chemical engineering problems that can be solved using numerica

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depen

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of S

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is

This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground, to reinforce for students that n

In this short monograph Newton-likeand other similar numerical methods with applications to solving multivariateequations are developed, which involve Caputotype fractional mixed partial derivatives a

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computation

Designed for a one-semester undergraduate introduction to numerical methods, this text covers both the theory and practice of numerical methods for mathematics and engineering. With a wealth of exerci

Multiphysics Modeling: Numerical Methods and Engineering Applications: Tsinghua University Press Computational Mechanics Series describes the basic principles and methods for multiphysics modeling, co

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely

This monograph presents recent original work in Numerical Analysis and Fractional Calculus. The chapters are self-contained and can be read independently. An extensive list of references is given per

The third edition of this successful text describes and evaluates a range of widely used numerical methods, with an emphasis on problem solving. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB® M-files accompany each method and are available on the book's web page. Code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method. The third edition features a new chapter on Euler's method, a number of new and improved examples and exercises, and programs which appear as function M-files. Numerical Methods in Engineering with MATLAB®, 3rd edition is a useful resource for both graduate students and practicing engineers.

The book not only offers scientists and engineers a clear inter-disciplinary introduction and orientation to all major EHL problems and their solutions but, most importantly, it also provides numerica

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis o

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis o

This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the

This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including:-The classical potential (incompressible)

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While th

Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in num

Based on the authors' experience teaching introductory numerical methods and optimization courses, this book covers numerical methods for Industrial and Systems Engineering and Operations Research. It

"Geared toward advanced undergraduates or graduate students of chemical engineering studying applied mathematics, this text introduces the quantitative treatment of differential equations arising from

"The objective of this book is for readers to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of the many techniques that are available

Numerical Methods for Engineers and Scientists, 3rd Edition provides engineers with a more concise treatment of the essential topics of numerical methods while emphasizing MATLAB use. The third editio

This book (along with vol. 2) covers most of the traditional methods for polynomial root-finding such as Newton's, as well as numerous variations on them invented in the last few decades. Perhaps more

"This book illustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally effic

The book introduces at a master's level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at student

"A practical, professional guide to MATLAB applications, numerical techniques, and scientific computing MATLAB Numerical Methods with Chemical Engineering Applications shows how to use MATLAB to mode

Focuses on basic lubrication problems and offers specific engineering applications. The book is divided into four parts. The first part is Reynolds equation solution, which includes solutions of Reyn

The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit wit

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems

Driven by concrete computational problems in quantitative finance, this book provides aspiring quant developers with the numerical techniques and programming skills they need. The authors start from scratch, so the reader does not need any previous experience of C++. Beginning with straightforward option pricing on binomial trees, the book gradually progresses towards more advanced topics, including nonlinear solvers, Monte Carlo techniques for path-dependent derivative securities, finite difference methods for partial differential equations, and American option pricing by solving a linear complementarity problem. Further material, including solutions to all exercises and C++ code, is available online. The book is ideal preparation for work as an entry-level quant programmer and it gives readers the confidence to progress to more advanced skill sets involving C++ design patterns as applied in finance.

Driven by concrete computational problems in quantitative finance, this book provides aspiring quant developers with the numerical techniques and programming skills they need. The authors start from scratch, so the reader does not need any previous experience of C++. Beginning with straightforward option pricing on binomial trees, the book gradually progresses towards more advanced topics, including nonlinear solvers, Monte Carlo techniques for path-dependent derivative securities, finite difference methods for partial differential equations, and American option pricing by solving a linear complementarity problem. Further material, including solutions to all exercises and C++ code, is available online. The book is ideal preparation for work as an entry-level quant programmer and it gives readers the confidence to progress to more advanced skill sets involving C++ design patterns as applied in finance.

The purpose of this book is to present the basic elements of numerical methods for compressible flows. It is appropriate for advanced undergraduate and graduate students and specialists working in high speed flows. The focus is on the unsteady one-dimensional Euler equations which form the basis for numerical algorithms in compressible fluid mechanics. The book is restricted to the basic concepts of finite volume methods, and even in this regard is not intended to be exhaustive in its treatment. Although the practical applications of the one-dimensional Euler equations are limited, virtually all numerical algorithms for inviscid compressible flow in two and three dimensions owe their origin to techniques developed in the context of the one-dimensional Euler equations. The author believes it is therefore essential to understand the development and implementation of these algorithms in their original one-dimensional context. The text is supplemented by numerous end-of-chapter exercises.