Eihab B. M. Bashier - Practical Numerical and Scientific Computing with Matlab® and Python

Practical Numerical and Scientific Computing with MATLAB and Python

Practical Numerical and Scientific Computing with MATLAB and Python

Eihab B. M. Bashier

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Library of Congress Cataloging-in-Publication Data

Names: Bashier, Eihab Bashier Mohammed, author.

Title: Practical Numerical and Scientific Computing with MATLAB and Python / Eihab B.M. Bashier.

Description: Boca Raton : CRC Press, 2020. | Includes bibliographical references and index.

Identifiers: LCCN 2019052363 | ISBN 9780367076696 (hardback) | ISBN 9780429021985 (ebook)

Subjects: LCSH: Science--Data processing. | MATLAB. | Python (Computer program language)

Classification: LCC Q183.9 B375 2020 | DDC 502.85/53--dc23

LC record available at https://lccn.loc.gov/2019052363

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Contents

The past few decades have witnessed tremendous development in the manufacture of computers and software, and scientific computing has become an important tool for finding solutions to scientific problems that come from various branches of science and engineering. Nowadays, scientific computing has become one of the most important means of research and learning in the fields of science and engineering, which are indispensable to any researcher, teacher, or student in the fields of science and engineering.

One of the most important branches of scientific computing is a numerical analysis which deals with the issues of finding approximate numerical solutions to such problems and analyzing errors related to such approximate methods. Both the MATLAB and Python programming languages provide many libraries that can be used to find solutions of scientific problems visualizing them. The ease of use of these two languages became the most languages that most scientists who use computers to solve scientific problems care about.

The idea of this book came after I taught courses of scientific computing for physics students, introductory and advanced courses in mathematical software and mathematical computer applications in many Universities in Africa and the gulf area. I also conducted some workshops for mathematics and science students who are interested in computational mathematics in some Sudanese Universities. In these courses and workshops, MATLAB and Python were used for the implementation of the numerical approximation algorithms. Hence, the purpose of introducing this book is to provide the student with a practical guide to solve mathematical problems using MATLAB and Python software without the need for third-party assistance. Since numerical analysis is concerned with the problems of approximation and analysis of errors of numerical methods associated with approximation methods, this book is more concerned with how these two aspects are applied in practice by software, where illustrations and tables are used to clarify approximate solutions, errors and speed of convergence, and its relations to some of the numerical method parameters, such as step size and tolerance. MATLAB and Python are the most popular programming languages for mathematicians, scientists, and engineers. Both the two programming languages possess various libraries for numerical and symbolic computations and data representation and visualization. Proficiency with the computer programs contained in this book requires that the student have prior knowledge of the basics of the programming languages MATLAB and Python, such as branching, Loops, symbolic packages, and the graphical libraries. The MATLAB version used for this book is 2017b and the Python version is 3.7.4.

The book consists of 11 chapters divided into three parts: the first part is concerned with discussing numerical solutions for linear and nonlinear systems and numerical difficulties facing these types of problems with how to overcome these numerical difficulties. The second part deals with methods of completing functions, differential and numerical integration, and solutions of differential equations. The last part of the book discusses methods to solve linear and nonlinear programming and optimal control problems. It also contains some specialized software in Python language to solve some problems numerically. These software packages must be downloaded from a third party, such as Gekko which is used for the solutions of differential equations and linear and nonlinear programming in addition to the optimal control problems. Also, the Pulp package is used to solve linear programming problems and finally Pyomo a package is used for solving linear and nonlinear programming problems. How to install and run such a package is also presented in the book.

What distinguishes this book from many other numerical analysis books is that it contains some topics that are not usually found in other books, such as nonstandard finite difference methods for solving differential equations and solutions of optimal control problems. In addition, the book discusses implementations of methods with high convergence rates, such as Gauss integration methods discussed in the numerical differentiation and integration, exact finite difference schemes for solving differential equations discussed in the nonstandard finite differences Chapter. It also uses efficient python-based software for solving some kinds of mathematical problems numerically.