rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Advanced numerical and semi analytical methods for differential equations
  name:
    name part: Chakraverty, Snehashish
    role:
      role term: author.
  type of resource: text
  origin info:
    place:
      place term: nju
    date issued: 2019
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: 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 …
  table of contents: Cover; Title Page; Copyright; Contents; Acknowledgments; Preface; Chapter 1 Basic Numerical Methods; 1.1 Introduction; 1.2 Ordinary Differential Equation; 1.3 Euler Method; 1.4 Improved Euler Method; 1.5 Runge-Kutta Methods; 1.5.1 Midpoint Method; 1.5.2 Runge-Kutta Fourth Order; 1.6 Multistep Methods; 1.6.1 Adams-Bashforth Method; 1.6.2 Adams-Moulton Method; 1.7 Higher-Order ODE; References; Chapter 2 Integral Transforms; 2.1 Introduction; 2.2 Laplace Transform; 2.2.1 Solution of Differential Equations Using Laplace Transforms; 2.3 Fourier Transform
  table of contents: 2.3.1 Solution of Partial Differential Equations Using Fourier TransformsReferences; Chapter 3 Weighted Residual Methods; 3.1 Introduction; 3.2 Collocation Method; 3.3 Subdomain Method; 3.4 Least-square Method; 3.5 Galerkin Method; 3.6 Comparison of WRMs; References; Chapter 4 Boundary Characteristics Orthogonal Polynomials; 4.1 Introduction; 4.2 Gram-Schmidt Orthogonalization Process; 4.3 Generation of BCOPs; 4.4 Galerkin's Method with BCOPs; 4.5 Rayleigh-Ritz Method with BCOPs; References; Chapter 5 Finite Difference Method; 5.1 Introduction; 5.2 Finite Difference Schemes
  table of contents: 5.2.1 Finite Difference Schemes for Ordinary Differential Equations5.2.1.1 Forward Difference Scheme; 5.2.1.2 Backward Difference Scheme; 5.2.1.3 Central Difference Scheme; 5.2.2 Finite Difference Schemes for Partial Differential Equations; 5.3 Explicit and Implicit Finite Difference Schemes; 5.3.1 Explicit Finite Difference Method; 5.3.2 Implicit Finite Difference Method; References; Chapter 6 Finite Element Method; 6.1 Introduction; 6.2 Finite Element Procedure; 6.3 Galerkin Finite Element Method; 6.3.1 Ordinary Differential Equation; 6.3.2 Partial Differential Equation
  table of contents: 6.4 Structural Analysis Using FEM6.4.1 Static Analysis; 6.4.2 Dynamic Analysis; References; Chapter 7 Finite Volume Method; 7.1 Introduction; 7.2 Discretization Techniques of FVM; 7.3 General Form of Finite Volume Method; 7.3.1 Solution Process Algorithm; 7.4 One-Dimensional Convection-Diffusion Problem; 7.4.1 Grid Generation; 7.4.2 Solution Procedure of Convection-Diffusion Problem; References; Chapter 8 Boundary Element Method; 8.1 Introduction; 8.2 Boundary Representation and Background Theory of BEM; 8.2.1 Linear Differential Operator; 8.2.2 The Fundamental Solution
  table of contents: 8.2.2.1 Heaviside Function8.2.2.2 Dirac Delta Function; 8.2.2.3 Finding the Fundamental Solution; 8.2.3 Green's Function; 8.2.3.1 Green's Integral Formula; 8.3 Derivation of the Boundary Element Method; 8.3.1 BEM Algorithm; References; Chapter 9 Akbari-Ganji's Method; 9.1 Introduction; 9.2 Nonlinear Ordinary Differential Equations; 9.2.1 Preliminaries; 9.2.2 AGM Approach; 9.3 Numerical Examples; 9.3.1 Unforced Nonlinear Differential Equations; 9.3.2 Forced Nonlinear Differential Equation; References; Chapter 10 Exp-Function Method; 10.1 Introduction; 10.2 Basics of Exp-Function Method
  note: Snehashish Chakraverty (National Institute of Technology Rourkela, Odisha, India) [and three others].
  note: Includes index.
  note: Includes bibliographical references and index.
  subject:
    topic: Differential equations
    topic: Numerical solutions
  classification: QA372 .A38 2019
  classification: QA372 .A338 2019e
  classification: 515/.35
  related item:
    title info:
      title: Advanced numerical and semi analytical methods for differential equations
    origin info:
      publisher: Hoboken, NJ : John Wiley & Sons, Inc., 2019
    identifier: (DLC) 2019000080
  identifier: 9781119423447
  identifier: 1119423449
  identifier: 9781119423430
  identifier: 1119423430
  identifier: 9781119423423 (hardcover)
  identifier: 9781119423461
  identifier: 1119423465
  identifier: 1119423422
  identifier: 2019022130
  identifier: 9781119423430 Wiley
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: DLC
    record creation date: 190506
    record change date: 20260214200150.6
    record identifier: in00004685839
    language of cataloging:
      language term: eng