# Advanced Numerical and Semi Analytical Methods for Differential Equations

• Publisher : John Wiley & Sons
• Release : 20 March 2019
• ISBN : 9781119423447
• Page : 256 pages
• Rating : 4.5/5 from 103 voters

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

### Advanced Numerical and Semi-Analytical Methods for Differential Equations • Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
• Publisher : John Wiley & Sons
• Release Date : 2019-03-20
• ISBN : 9781119423447

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods

### Weighted Residual Methods • Release Date : 2017-11-07
• ISBN : 9780128132197

Weighted Residual Methods: Principles, Modifications and Applications introduces a range of WRMs, providing examples that show how they can be used to solve complex engineering problems with greater accuracy and computational efficiency. Examples focus on non-linear problems, including the motion of a spherical particle, nanofluid flow and heat transfer, magnetohydrodynamic flow and heat transfer, and micropolar fluid flow and heat transfer. These are important factors in understanding processes, such as filtration, combustion, air and water pollution and micro contamination. In

### The Finite Element Method • Author : Zhu
• Publisher : John Wiley & Sons
• Release Date : 2018-03-12
• ISBN : 9781119107330

A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would

### The Method of Weighted Residuals and Variational Principles • Author : Bruce A. Finlayson
• Publisher : SIAM
• Release Date : 2013-12-30
• ISBN : 9781611973235

This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element

### The Finite Element Method in Engineering • Author : Singiresu S. Rao
• Publisher : Elsevier
• Release Date : 2011-03-15
• ISBN : 9780080470504

The Finite Element Method in Engineering is the only book to provide a broad overview of the underlying principles of finite element analysis and where it fits into the larger context of other mathematically based engineering analytical tools. This is an updated and improved version of a finite element text long noted for its practical applications approach, its readability, and ease of use. Students will find in this textbook a thorough grounding of the mathematical principles underlying the popular, analytical

### The Method of Weighted Residuals and Variational Principles • Author : Bruce A. Finlayson
• Publisher : SIAM
• Release Date : 2013-12-30
• ISBN : 9781611973242

This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element

### Adaptive Finite Element Methods for Differential Equations • Author : Wolfgang Bangerth,Rolf Rannacher
• Publisher : Birkhäuser
• Release Date : 2013-11-11
• ISBN : 9783034876056

These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted

### Introduction to Numerical Methods for Variational Problems • Author : Hans Petter Langtangen,Kent-Andre Mardal
• Publisher : Springer Nature
• Release Date : 2019-09-26
• ISBN : 9783030237882

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally

### The Method of Weighted Residuals and Variational Principles • Author : Bruce A. Finlayson
• Publisher : Bruce Alan Finlayson
• Release Date : 1972
• ISBN : 0122570502

The method of weighted residuals and variational principles, with application in fluid mechanics, heat and mass transfer

### TEXTBOOK OF FINITE ELEMENT ANALYSIS • Author : P. SESHU
• Publisher : PHI Learning Pvt. Ltd.
• Release Date : 2003-01-01
• ISBN : 9788120323155

Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and

### Numerical Methods for Engineers and Scientists • Author : Joe D. Hoffman,Steven Frankel
• Publisher : CRC Press
• Release Date : 2018-10-03
• ISBN : 9781482270600

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study

### Energy Principles and Variational Methods in Applied Mechanics • Author : J. N. Reddy
• Publisher : John Wiley & Sons
• Release Date : 2017-09-05
• ISBN : 9781119087380

A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineering problems involving bars, beams, torsion, plane elasticity, trusses, and plates. It begins with a review of the basic equations of mechanics, the concepts of work and energy, and key topics from variational calculus. It presents virtual work

### The Finite Element Method Using MATLAB • Author : Young W. Kwon,Hyochoong Bang
• Publisher : CRC Press
• Release Date : 2018-10-03
• ISBN : 1420041886

Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis. What's new in the Second Edition? Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each

### Computational Fluid Dynamics • Author : T. J. Chung
• Publisher : Cambridge University Press
• Release Date : 2010-09-27
• ISBN : 9781139493291

The second edition of Computational Fluid Dynamics represents a significant improvement from the first edition. However, the original idea of including all computational fluid dynamics methods (FDM, FEM, FVM); all mesh generation schemes; and physical applications to turbulence, combustion, acoustics, radiative heat transfer, multiphase flow, electromagnetic flow, and general relativity is still maintained. The second edition includes a new section on preconditioning for EBE-GMRES and a complete revision of the section on flowfield-dependent variation methods, which demonstrates more detailed computational

### A Finite Element Primer for Beginners • Author : Tarek I. Zohdi
• Publisher : Springer
• Release Date : 2014-08-12
• ISBN : 9783319090368

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: (1) Weighted residual methods and Galerkin approximations, (2) A model problem for one-dimensional linear elastostatics, (3) Weak formulations in one dimension, (4) Minimum principles in one dimension, (5) Error estimation in one dimension, (5) Construction of Finite Element basis functions in one dimension, (6) Gaussian Quadrature, (7) Iterative solvers and element by element data structures, (8) A model problem for three-dimensional