Numerical Methods with Matlab

Description

Canada, University of Ottawa, 2009, 189 p.Учебник по численным методам с примерами на Matlab. Хорошо изложено "Численное дифференцирование и интегрирование" ( "Numerical Differentiation and Integration"). Глава 6 ("The Matlab ODE Suite"), написанная на основе известной статьи авторов, посвящена сравнению Matlab-программ для решения обыкновенных дифференциальных уравнений.Contents _Solutions of Nonlinear Equations Computer Arithmetics Review of Calculus The Bisection Method Fixed Point Iteration Newton’s, Secant, and False Position Methods Accelerating Convergence Horner’s Method and the Synthetic Division Muller’s Method _Interpolation and Extrapolation Lagrange Interpolating Polynomial Newton’s Divided Difference Interpolating Polynomial Gregory–Newton Forward-Difference Polynomial Gregory–Newton Backward-Difference Polynomial Hermite Interpolating Polynomial Cubic Spline Interpolation _ Numerical Differentiation and Integration Numerical Differentiation The Effect of Roundoff and Truncation Errors Richardson’s Extrapolation Basic Numerical Integration Rules The Composite Midpoint Rule The Composite Trapezoidal Rule The Composite Simpson’s Rule Romberg Integration for the Trapezoidal Rule Adaptive Quadrature Methods _Matrix Computations LU Solution of Ax = b Cholesky Decomposition Matrix Norms Iterative Methods Overdetermined Systems Matrix Eigenvalues and Eigenvectors The QR Decomposition The QR algorithm The Singular Value Decomposition _Numerical Solution of Differential Equations Initial Value Problems Euler’s and Improved Euler’s Method Low-Order Explicit Runge–Kutta Methods Convergence of Numerical Methods Absolutely Stable Numerical Methods Stability of Runge–Kutta methods Embedded Pairs of Runge–Kutta methods Multistep Predictor-Corrector Methods Stiff Systems of Differential Equations _ The Matlab ODE Suite Introduction The Methods in the Matlab ODE Suite The odeset Options Nonstiff Problems of the Matlab odedemo Stiff Problems of the Matlab odedemo Concluding Remarks Bibliography _ Orthogonal polynomials Fourier–Legendre Series Derivation of Gaussian Quadratures Numerical Solution of Integral Equations of the Second Kind _Formulae and Tables Legendre Polynomials Pn(x) on [−1, 1] Laguerre Polynomials on 0 ≤ x ∞ Fourier–Legendre Series Expansion Exercises for Numerical Methods Solutions to Exercises for Numerical Methods Index