DOS NOVEDADES DE ANALISIS NUMERICO DE JOHN WILEY

DOS NOVEDADES DE ANALISIS NUMERICO DE JOHN WILEY

ADVANCED NUMERICAL AND SEMI ANALYTICAL METHODS FOR DIFFERENTIAL EQUATIONS

Snehashish Chakraverty (National Institute of Techniology Rourkela, Odisha, India)       

Hoboken, NJ. USA. JOHN WILEY. ISBN 9781119423423. 256 págs. Julio de 2019. Encuadernado

PVP EUR 109,00 (4% IVA incluido)

Este libro cubre los métodos que se pueden usar para resolver diferentes ecuaciones diferenciales parciales y ordinarias tanto lineales como no lineales.

 

Extracto del índice:

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

 

NUMERICAL ANALYSIS FOR APPLIED SCIENCE. 2nd Edition

Myron B. Allen, Eli L. Isaacson (University of Wyoming, Laramie, WY, USA)

Hoboken, NJ, USA. JOHN WILEY. ISBN 9781119245469. 576 págs. Abril de 2019. Encuadernado                                                                                                       

PVP EUR 128,00 (4% IVA incluido)

Les ofrecemos un nuevo volumen de la serie PURE AND APPLIED MATHEMATICS. Podemos enviarles más información sobre otros volúmenes, si así nos lo indican.

Esta edición actualizada y ampliada sigue la tradición de su precursor al proporcionar un enfoque moderno y flexible a la teoría y las aplicaciones prácticas del campo. Se enfatizan la motivación, la construcción y las consideraciones prácticas antes de presentar un análisis teórico riguroso.

 

Extracto del índice:

Preface

1 Some Useful Tools

1.1 Introduction

1.2 Bounded Sets

1.3 Normed Vector Spaces

1.4 Eigenvalues and Matrix Norms

1.5 Results from Calculus

1.6 Problems

2 Approximation of Functions

2.1 Introduction

2.2 Polynomial Interpolation

2.3 Piecewise Polynomial Interpolation

2.4 Hermite Interpolation

2.5 Interpolation in Two Dimensions

2.6 Splines

2.7 LeastSquares Methods

2.8 Trigonometric Interpolation

2.9 Problems

3 Direct Methods for Linear Systems

3.1 Introduction

3.2 The Condition Number of a Linear System

3.3 Gauss Elimination

3.4 Variants of Gauss Elimination

3.5 Band Matrices

3.6 Iterative Improvement

3.7 Problems

4 Solution of Nonlinear Equations

4.1 Introduction

4.2 Bisection

4.3 Successive Substitution in One Variable

4.4 Newton’s Method in One Variable

4.5 The Secant Method

4.6 Successive Substitution: Several Variables

4.7 Newton’s Method: Several Variables

4.8 Problems

5 Iterative Methods for Linear Systems

5.1 Introduction

5.2 Conceptual Foundations

5.3 MatrixSplitting Techniques

5.4 Successive Overrelaxation

5.5 Multigrid Methods

5.6 The ConjugateGradient Method

5.7 Problems

6 Eigenvalue Problems

6.1 More About Eigenvalues

6.2 Power Methods

6.3 The QR Decomposition

6.4 The QR Algorithm for Eigenvalues

6.5 Singular Value Decomposition

6.6 Problems

7 Numerical Integration

7.1 Introduction

7.2 NewtonCotes Formulas

7.3 Romberg and Adaptive Quadrature

7.4 Gauss Quadrature

7.5 Problems

8 Ordinary Differential Equations

8.1 Introduction

8.2 OneStep Methods

8.3 Multistep Methods: Consistency and Stability

8.4 Multistep Methods: Convergence

8.5 Problems

9 Difference Methods for PDEs

9.1 Introduction

9.2 The Poisson Equation

9.3 The Advection Equation

9.3.4 Further Remarks

9.5 Problems

10 Introduction to Finite Elements

10.1 Introduction and Background

10.2 A SteadyState Problem

10.3 A Transient Problem

10.4 Problems

A Divided Differences

B Local Minima

C Chebyshev Polynomials

References

Index

 

 

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