Numerical Methods for Engineers and Scientists Using MATLAB

TLDR: This chapter discusses Numerical Solution of Partial Differential Equations, a method for estimating the Eigenvalue of a Single Variable Equations using Newton-Cotes Formulas.

Abstract: Background and Introduction Background Introduction to Numerical Methods Problem Set Introduction to MATLAB(R) MATLAB(R) Built-In Functions Vectors and Matrices User-Defined Functions and Script Files Program Flow Control Displaying Formatted Data Symbolic Toolbox Plotting Problem Set Solution of Equations of a Single Variable Numerical Solution of Equations Bisection Method Regula Falsi Method (Method of False Position) Fixed-Point Method Newton's Method (Newton-Raphson Method) Secant Method Equations with Several Roots Problem Set Solution of Systems of Equations Linear Systems of Equations Numerical Solution of Linear Systems Gauss Elimination Method LU Factorization Methods Iterative Solution of Linear Systems Ill-Conditioning and Error Analysis Systems of Nonlinear Equations Problem Set Curve Fitting (Approximation) and Interpolation Least-Squares Regression Linear Regression Linearization of Nonlinear Data Polynomial Regression Polynomial Interpolation Spline Interpolation Fourier Approximation and Interpolation Problem Set Numerical Differentiation and Integration Numerical Differentiation Finite-Difference Formulas for Numerical Differentiation Numerical Integration: Newton-Cotes Formulas Numerical Integration of Analytical Functions: Romberg Integration, Gaussian Quadrature Improper Integrals Problem Set Numerical Solution of Initial-Value Problems One-Step Methods Euler's Method Runge-Kutta Methods Multistep Methods Systems of Ordinary Differential Equations Stability Stiff Differential Equations MATLAB(R) Built-In Functions for Initial-Value Problems Problem Set Numerical Solution of Boundary-Value Problems Shooting Method Finite-Difference Method BVPs with Mixed Boundary Conditions MATLAB(R) Built-In Function bvp4c for BVPs Problem Set Matrix Eigenvalue Problem Power Method: Estimation of the Dominant Eigenvalue Deflation Methods Householder Tridiagonalization and QR Factorization Methods Problem Set Numerical Solution of Partial Differential Equations Introduction Elliptic PDEs Parabolic PDEs Hyperbolic PDEs Problem Set Bibliography Index