PL06, Numerical methods
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Contents
- Introduction
- Number System and Errors
- Roots of Equations
- System of Linear Equations
- Interpolation
- Interpolation with Spline Functions
- The Method of Least-Squares
- Numerical Optimization
- Numerical Differentiation
- Numerical Integration
- Numerical Methods for Linear Integral Equations
- Numerical Methods for Differential Equations
- EULER’S METHOD
- ERROR ANALYSIS
- HIGHER-ORDER TAYLOR SERIES METHODS
- RUNGE-KUTTA METHODS
- MULTISTEP METHODS
- ADAMS-BASHFORTH METHODS
- PREDICTOR-CORRECTOR METHODS
- ADAMS-MOULTON METHODS
- NUMERICAL STABILITY
- HIGHER-ORDER EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS
- IMPLICIT METHODS AND STIFF SYSTEMS
- PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS
- Boundary-Value Problems
- Eigenvalues and Eigenvectors
- Dynamical Systems and Chaos
- Partial Differential Equations
Introduction
| Region | Command |
|---|---|
| workspace | workspace, clear |
| script | edit,ctrl + n |
| CLI | clc |
| current folder | filebrowser |
ABOUT MATLAB and MATLAB GUI (Graphical User Interface)
AN INTRODUCTION TO MATLAB
TAYLOR SERIES
Number System and Errors
FLOATING-POINT ARITHMETIC
ROUND-OFF ERRORS
TRUNCATION ERROR
INTERVAL ARITHMETIC
Roots of Equations
THE BISECTION METHOD
FIXED POINT ITERATION
THE SECANT METHOD
NEWTON’S METHOD
CONVERGENCE OF THE NEWTON AND SECANT METHODS
MULTIPLE ROOTS AND THE MODIFIED NEWTON METHOD
NEWTON’S METHOD FOR NONLINEAR SYSTEMS
System of Linear Equations
MATRICES AND MATRIX OPERATIONS
NAIVE GAUSSIAN ELIMINATION
GAUSSIAN ELIMINATION WITH SCALED PARTIAL PIVOTING
LU DECOMPOSITION
ITERATIVE METHODS
Interpolation
POLYNOMIAL INTERPOLATION THEORY
NEWTON’S DIVIDED-DIFFERENCE INTERPOLATING POLYNOMIAL
THE ERROR OF THE INTERPOLATING POLYNOMIAL
LAGRANGE INTERPOLATING POLYNOMIAL
Interpolation with Spline Functions
PIECEWISE LINEAR INTERPOLATION
QUADRATIC SPLINE
NATURAL CUBIC SPLINES
The Method of Least-Squares
LINEAR LEAST-SQUARES
LEAST-SQUARES POLYNOMIAL
NONLINEAR LEAST-SQUARES
Numerical Optimization
ANALYSIS OF SINGLE-VARIABLE FUNCTIONS
LINE SEARCH METHODS
MINIMIZATION USING DERIVATIVES
Numerical Differentiation
NUMERICAL DIFFERENTIATION
RICHARDSON’S FORMULA
Numerical Integration
TRAPEZOIDAL RULE
SIMPSON’S RULE
ROMBERG ALGORITHM
GAUSSIAN QUADRATURE
Numerical Methods for Linear Integral Equations
INTRODUCTION
QUADRATURE RULES
THE SUCCESSIVE APPROXIMATION METHOD
SCHMIDT’s METHOD
VOLTERRA-TYPE INTEGRAL EQUATIONS
Numerical Methods for Differential Equations
EULER’S METHOD
ERROR ANALYSIS
HIGHER-ORDER TAYLOR SERIES METHODS
RUNGE-KUTTA METHODS
MULTISTEP METHODS
ADAMS-BASHFORTH METHODS
PREDICTOR-CORRECTOR METHODS
ADAMS-MOULTON METHODS
NUMERICAL STABILITY
HIGHER-ORDER EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS
IMPLICIT METHODS AND STIFF SYSTEMS
PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS
Boundary-Value Problems
FINITE-DIFFERENCE METHODS
SHOOTING METHODS
Eigenvalues and Eigenvectors
BASIC THEORY
THE POWER METHOD
THE QUADRATIC METHOD
EIGENVALUES FOR BOUNDARY-VALUE PROBLEMS
BIFURCATIONS IN DIFFERENTIAL EQUATIONS
Dynamical Systems and Chaos
A REVIEW OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS
DEFINITIONS AND THEORETICAL CONSIDERATIONS
TWO-DIMENSIONAL SYSTEMS
CHAOS
LAGRANGIAN DYNAMICS
Partial Differential Equations
PARABOLIC EQUATIONS
HYPERBOLIC EQUATIONS
ELLIPTIC EQUATIONS
NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
INTRODUCTION TO FINITE-ELEMENT METHOD
List of posts followed by this article
Reference
- matlab
- matlab, basic
- matlab, document
- Dr. Abdelwahab Kharab, Professor Ronald B. Guenther, An Introduction to Numerical Methods
OUTPUT
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