book

Advanced Numerical and Semi-Analytical Methods for Differential Equations

April 2019

Intermediate to advanced

256 pages

5h 48m

English

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1.1 Introduction1.2 Ordinary Differential Equation1.3 Euler Method1.4 Improved Euler Method1.5 Runge–Kutta Methods1.6 Multistep Methods1.7 Higher‐Order ODEReferences
2.1 Introduction2.2 Laplace Transform2.3 Fourier TransformReferences
3.1 Introduction3.2 Collocation Method3.3 Subdomain Method3.4 Least‐square Method3.5 Galerkin Method3.6 Comparison of WRMsExerciseReferences
4.1 Introduction4.2 Gram–Schmidt Orthogonalization Process4.3 Generation of BCOPs4.4 Galerkin's Method with BCOPs4.5 Rayleigh–Ritz Method with BCOPsExerciseReferences
5.1 Introduction5.2 Finite Difference Schemes5.3 Explicit and Implicit Finite Difference SchemesReferences
6.1 Introduction6.2 Finite Element Procedure6.3 Galerkin Finite Element Method6.4 Structural Analysis Using FEMReferences
7.1 Introduction7.2 Discretization Techniques of FVM7.3 General Form of Finite Volume Method7.4 One‐Dimensional Convection–Diffusion ProblemReferences

8.1 Introduction8.2 Boundary Representation and Background Theory of BEM8.3 Derivation of the Boundary Element MethodReferences
9.1 Introduction9.2 Nonlinear Ordinary Differential Equations9.3 Numerical ExamplesReferences
10.1 Introduction10.2 Basics of Exp‐Function Method10.3 Numerical ExamplesReferences
11.1 Introduction11.2 ADM for ODEs11.3 Solving System of ODEs by ADM11.4 ADM for Solving Partial Differential Equations11.5 ADM for System of PDEsExerciseReferences
12.1 Introduction12.2 Basic Idea of HPM12.3 Numerical ExamplesReferences
13.1 Introduction13.2 VIM Procedure13.3 Numerical ExamplesReferences
14.1 Introduction14.2 HAM Procedure14.3 Numerical ExamplesExerciseReferences
15.1 Introduction15.2 DQM Procedure15.3 Numerical ExamplesReferences
16.1 Introduction16.2 Haar Wavelet16.3 Wavelet–Collocation MethodExerciseReferences
17.1 Introduction17.2 Homotopy Perturbation Transform Method17.3 Laplace Adomian Decomposition MethodReferences
18.1 Introduction to Fractal18.2 Fractal Differential EquationsReferences
19.1 Introduction19.2 Interval Differential Equations19.3 Generalized Hukuhara Differentiability of IDEs19.4 Analytical Methods for IDEsReferences
20.1 Introduction20.2 Solving Fuzzy Linear System of Differential EquationsReferences
21.1 Introduction21.2 Interval Galerkin FEM21.3 Structural Analysis Using IFEMReferences