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| Author | : T.Y. Na |
| Publisher | : Academic Press |
| Total Pages | : 321 |
| Release | : 1980-01-18 |
| Genre | : Computers |
| ISBN | : 008095653X |
Computational Methods in Engineering Boundary Value Problems
| Author | : S. P. Venkateshan |
| Publisher | : Springer Nature |
| Total Pages | : 824 |
| Release | : 2023-05-31 |
| Genre | : Technology & Engineering |
| ISBN | : 3031082265 |
The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial value problems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.
| Author | : Uri M. Ascher |
| Publisher | : SIAM |
| Total Pages | : 620 |
| Release | : 1994-12-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971231 |
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
| Author | : Paul Farrell |
| Publisher | : CRC Press |
| Total Pages | : 298 |
| Release | : 2000-03-30 |
| Genre | : Science |
| ISBN | : 9781584881926 |
Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques. Focusing on robustness, simplicity, and wide applicability rather than on optimality, Robust Computational Techniques for Boundary Layers provides readers with an understanding of the underlying principles and the essential components needed for the construction of numerical methods for boundary layer problems. It explains the fundamental ideas through physical insight, model problems, and computational experiments and gives details of the linear solvers used in the computations so that readers can implement the methods and reproduce the numerical results.
| Author | : Ali Ümit Keskin |
| Publisher | : Springer |
| Total Pages | : 517 |
| Release | : 2019-06-19 |
| Genre | : Technology & Engineering |
| ISBN | : 3030210804 |
This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).
| Author | : Herbert B. Keller |
| Publisher | : SIAM |
| Total Pages | : 69 |
| Release | : 1976-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970449 |
Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
| Author | : Karan S. Surana |
| Publisher | : CRC Press |
| Total Pages | : 824 |
| Release | : 2016-11-17 |
| Genre | : Science |
| ISBN | : 1498780512 |
Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.
| Author | : R. P. Agarwal |
| Publisher | : |
| Total Pages | : |
| Release | : 1983 |
| Genre | : |
| ISBN | : |
| Author | : O. Axelsson |
| Publisher | : SIAM |
| Total Pages | : 452 |
| Release | : 2001-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898714990 |
a thorough, balanced introduction to both the theoretical and the computational aspects of the topic.
| Author | : Mohamed Zerroukat |
| Publisher | : Research Studies PressLtd |
| Total Pages | : 212 |
| Release | : 1994 |
| Genre | : Technology & Engineering |
| ISBN | : 9780863801686 |
This book reviews and compares some well-known numerical methods and more recent contributions for solving both moving boundary and boundary value problems. Recent advances in the finite difference solution of linear and non-linear partial differential equations are also presented and algorithmic manipulations which enhance the computational efficiency are incorporated into the overall schemes.
