Advanced numerical and semi analytical methods for differential equations 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 Galerkins Method with BCOPs; 4.5 Rayleigh Ritz Method with BCOPs; References; Chapter 5 Finite Difference Method; 5.1 Introduction; 5.2 Finite Difference Schemes 8.2.2.1 Heaviside Function8.2.2.2 Dirac Delta Function; 8.2.2.3 Finding the Fundamental Solution; 8.2.3 Greens Function; 8.2.3.1 Greens Integral Formula; 8.3 Derivation of the Boundary Element Method; 8.3.1 BEM Algorithm; References; Chapter 9 Akbari Ganjis 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 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 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 Ganjis 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 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 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