Snehashish Chakraverty & Nisha Mahato 
Advanced Numerical and Semi-Analytical Methods for Differential Equations [EPUB ebook] 

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
1.6 Multistep methods
1.7 Higher order ODE
2 Integral Transforms
2.1 Introduction
2.2 Laplace Transform
2.3 Fourier Tranform
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
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 BCOP’s
5 Finite Difference Method
5.1 Introduction
5.2 Finite Difference Scheme
5.3 Explicit and Implicit Finite Difference Schemes
6 Finite Element Method
6.1 Introduction
6.2 Finite element procedure
6.3 Galerkin finite element method
6.4 Structural analysis using FEM
7 Finite Volume Method
7.1 Introduction
7.2 Discretization Techniques of FVM
7.3 General Form of Finite Volume Method
7.4 One Dimensional Convection-diffusion problem
8 Boundary Element Method
8.1 Introduction
8.2 Boundary Representation and Background Theory of BEM
8.3 Derivation of the Boundary Element Method
9 Akbari Ganji’s Method
9.1 Introduction
9.2 Nonlinear ordinary differential equations
9.3 Numerical examples
10 Exp-function Method
10.1 Introduction
10.2 Basics of Exp-fucntion method
10.3 Numerical examples
11 Adomian Decomposition Method
11.1 Introduction
11.2 ADM for Ordinary Differential Equations (ODEs)
11.3 Solving system of ODEs by ADM
11.4 ADM for solving Partial Differential Equations (PDEs)
11.5 ADM for system of PDEs
12 Homotopy Perturbation Method
12.1 Introduction
12.2 Basic idea of HPM
12.3 Numerical examples
13 Variational Iteration Method
13.1 Introduction
13.2 VIM procedure
13.3 Numerical examples
14 Homotopy Analysis Method
14.1 Introduction
14.2 HAM procedure
14.3 Numerical examples
15 Differential Quadrature Method
15.1 Introduction
15.2 DQM procedure
15.3 Numerical examples
16 Wavelet Method
16.1 Introduction
16.2 Haar wavelet
16.3 Wavelet-collocation method
17 Hybrid Methods
17.1 Introduction
17.2 Homotopy Perturbation Transform Method
17.3 Laplace Adomian Decomposition Method
18 Preliminaries of Fractal Differential Equations
18.1 Introduction to fractal
18.2 Fractal differential equations
19 Differential Equations with Interval Uncertainty
19.1 Introduction
19.2 Interval Differential Equations (IDEs)
19.3 Generalized Hukuhara Differentiability of IDEs
19.4 Analytical Methods for IDEs
20 Differential Equations with Fuzzy Uncertainty
20.1 Solving Fuzzy Linear System of Differential Equations
21 Interval Finite Element Method
21.1 Introduction
21.2 Interval Galerkin FEM
21.3 Structural analysis using IFEM

SNEHASHISH CHAKRAVERTY, PHD, is Professor in the Department of Mathematics at National Institute of Technology, Rourkela, Odisha, India. He is also the author of Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications and 12 other books.
NISHA RANI MAHATO is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology, Rourkela, Odisha, India where she is pursuing her Ph D.
PERUMANDLA KARUNAKAR is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology, Rourkela, Odisha, India where he is pursuing his Ph D.
THARASI DILLESWAR RAO, is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology, Rourkela, Odisha, India where he is pursuing his Ph D.