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This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.
Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.
The book collects original articles on numerical analysis of ordinary differential equations and its applications. Some of the topics covered in this volume are: discrete variable methods, Runge-Kutta methods, linear multistep methods, stability analysis, parallel implementation, self-validating numerical methods, analysis of nonlinear oscillation by numerical means, differential-algebraic and delay-differential equations, and stochastic initial value problems.
Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. a unique blend of theory and applications two brand new chapters on eigenvalues and splines inclusion of formal algorithms numerous fully worked examples a large number of problems, many with solutions
The book collects original articles on numerical analysis of ordinary differential equations and its applications. Some of the topics covered in this volume are: discrete variable methods, Runge-Kutta methods, linear multistep methods, stability analysis, parallel implementation, self-validating numerical methods, analysis of nonlinear oscillation by numerical means, differential-algebraic and delay-differential equations, and stochastic initial value problems.
This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.
Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including: • a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption. This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.