 • Author : Snehashish Chakraverty
• Release Date : 20 March 2019
• Publisher : John Wiley & Sons
• Genre : Mathematics
• Pages : 256
• ISBN 13 : 9781119423447

## Advanced Numerical and Semi-Analytical Methods for Differential Equations Book Summary

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
Genre : Mathematics
Total View : 4443 Views
File Size : 53,5 Mb

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 ... ### Weighted Residual Methods

Genre : Technology & Engineering
Total View : 1058 Views
File Size : 47,7 Mb

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 ... ### The Method of Weighted Residuals and Variational Principles

Author : Bruce A. Finlayson
Publisher : SIAM
Genre : Mathematics
Total View : 2359 Views
File Size : 47,5 Mb

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 ... ### The Finite Element Method

Author : Zhu
Publisher : John Wiley & Sons
Genre : Mathematics
Total View : 4784 Views
File Size : 44,8 Mb

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 ... ### Introduction to Finite Element Analysis and Design

Author : Nam H. Kim,Bhavani V. Sankar,Ashok V. Kumar
Publisher : John Wiley & Sons
Genre : Technology & Engineering
Total View : 1573 Views
File Size : 49,5 Mb

Introduces the basic concepts of FEM in an easy-to-use format so that students and professionals can use the method efficiently and interpret results properly Finite element method (FEM) is a powerful tool for solving engineering problems both in solid structural mechanics and fluid mechanics. This book presents all of the ... ### The Finite Element Method in Engineering

Author : Singiresu S. Rao
Publisher : Elsevier
Genre : Technology & Engineering
Total View : 4130 Views
File Size : 49,7 Mb

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 ... ### Adaptive Finite Element Methods for Differential Equations

Author : Wolfgang Bangerth,Rolf Rannacher
Publisher : Birkhäuser
Genre : Mathematics
Total View : 379 Views
File Size : 52,6 Mb

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 ... ### The Method of Weighted Residuals and Variational Principles

Author : Bruce A. Finlayson
Publisher : SIAM
Genre : Mathematics
Total View : 8098 Views
File Size : 42,5 Mb

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 ...