Introduction to Numerical Methods in Differential Equations (Texts in Applied Mathematics)

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APPM 5610, Numerical Analysis 2, Spring 2018

Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering. Kendall E. He has authored books and journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods.

Prerequisites

Han currently focuses his research on the numerical solution of partial differential equations. David E. Stewart's research interests include numerical analysis, computational models of mechanics, scientific computing, and optimization.

Boundary value problems. Linear shooting method. Nonlinear shooting method. Finite difference methods for linear BVP.

Numerical Methods for Differential Equations - Home

Finite-difference methods for nonlinear BVP. Solving nonlinear systems of equations. Newton's method. Quasi-Newton method - Broyden's method. Homotopy and continuation methods. Linear algebra, Eigenvalues, orthogonal matrices and similarity transformations.

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Power method. Inverse Power method. Householder's transformation.


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Householder's method. QR factorization. QR algorithm.

Discrete least squares approximation. Linearly independent functions.

Applied Mathematics - Introduction to Numerical Analysis & Scientific Computing

Orthogonal polynomials and least squares approximation. Continuous and discrete trigonometric polynomial approximation.


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