Higgs Boson : a mathematical survey with finite element method / Harun Selvitopi.

Format:

Book

Author/Creator:

Selvitopi, Harun, author.

Series:

Computational Mathematics and Analysis Series

Language:

English

Subjects (All):

Finite element method.

Engineering mathematics.

Physical Description:

1 online resource (99 pages)

Edition:

1st ed.

Place of Publication:

New York, NY : Nova Science Publishers, Inc., [2023]

Summary:

In this book, the finite difference, finite element and the root finding approximations i.e. Newton, Quasi Newton and Broyden methods has been presented. We also consider the finite difference/finite element hybrid method to solve the wave equation in Einstein and de Sitter space-time. The mathematical model of the Higgs Boson equation in de Sitter space-time has been presented as a chapter. Finally, the finite difference/finite element solution using Newton linearization method has been presented.

Contents:

Cover

Half Title

Title Page

Copyright Page

Contents

Preface

Introduction

Chapter 1: Finite Difference Method for the Solution of Partial Differential Equations (PDE)

1.1 FDM for Elliptic Equations

1.2 FDM for Parabolic Equations

1.2.1 Forward-Difference Method

1.2.2 Backward-Difference Method

1.2.3 Crank-Nicolson Method

1.2.4 Stability Analysis of Finite Difference Method

1.2.5 Exercises

1.3 FDM for Hyperbolic Partial Differential Equations

1.3.1 Stability Analysis

Chapter 2: Finite Element Method for the Solution of Partial Differential Equations (PDE)

2.1 The Development of the Finite Element Method

2.2 Application of Finite Element Method to Partial Differential Equations

2.2.1 Discretization

2.2.2 Elements

2.2.3 2-D Elements

2.2.4 Shape Functions

2.2.5 Triangular Elements Shape Functions

2.2.6 Finite Element Method Formulation for Laplace Equation

2.2.7 Weak Form for Laplace Equation

2.2.8 Variational Form for Laplace Equation

Chapter 3: The Numerical Integration Methods

3.1 Newton-Type Integration Methods

3.1.1 Trapezium Rule

3.1.2 Simpson Method

3.2 Gauss-Type Integration Methods

3.2.1 Gauss-Legendre Method

3.3 Two-Dimensional Numerical Integration

Chapter 4: Finite Element Method Solution of Laplace Equation

Chapter 5: One-Dimensional Wave Equation

5.1 Finite Element Solution of One-Dimensional Wave Equation

5.2 Central Difference Approximation

Chapter 6: Finite Element Simulation of the One- and Two-Dimensional Wave Equation in Einstein and de Sitter Space-Time

6.1 Application of the Numerical Method for One-Dimensional Problem

6.2 Application of the Numerical Method for Two-Dimensional Problem

Chapter 7: Root Finding Approximations

7.1 Newton's Method

Application of Newton Method

7.2 Secant Method.

Chapter 8: Newton's Method for Nonlinear System of Equations in n-Dimension

8.1 Newton Method

8.2 Quasi-Newton Method

8.3 Broyden Method

Chapter 9: Finite Difference/Galerkin Finite Element Simulation of the Semi-Linear Wave Equation with Scale-Invariant Damping, Mass and Power Nonlinearity

9.1 Application of the GFEM

9.2 Application of the FDM

9.3 Application of Newton Method

Chapter 10: Higgs Boson in de Sitter Space-Time

10.1 Mathematical Model of the Higgs Boson in de Sitter Space-Time

10.2 Finite Element Method for Higgs Boson Equation

10.2.1 Newton Method

10.3 Numerical Results

References

Index

Blank Page.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Selvitopi, Harun Higgs Boson: a Mathematical Survey with Finite Element Method

ISBN:

979-88-911-3063-0