Advanced numerical and semi analytical methods for differential equations - Chakraverty, Snehashish (Hoboken, NJ : John Wiley & Sons, Inc., 2019)
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.
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
Includes index.
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Includes bibliographical references and index.
Keywords: Differential equations -- Numerical solutions; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Differential equations; Electronic books