Scientific Computing and Differential Equations: An Introduction to Numerical MethodsScientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also wellsuited to serve as a textbook for numerical differential equations courses at the graduate level.

What people are saying  Write a review
We haven't found any reviews in the usual places.
Contents
1  
15  
Boundary Value Problems  67 
Chapter 4 More on Linear Systems of
Equations  89 
Chapter 5
Life Is Really Nonlinear  145 
Chapter 6 Is There More Than Finite
Differences?  179 
Chapter 7
N Important Numbers  211 
Chapter 8
Space and Time  247 
Chapter 9 The Curse of Dimensionality  273 
Analysis and Differential Equations  309 
Linear Algebra  315 
Bibliography  321 
Author Index  329 
Subject Index  333 
Other editions  View all
Scientific Computing and Differential Equations: An Introduction to ... Gene H. Golub,James M. Ortega No preview available  1991 
Common terms and phrases
algorithm applied approximate solution assume banded matrix basis functions boundary conditions boundaryvalue problem Chapter coefficient matrix column consider corresponding cubic spline defined derivatives diagonally dominant difference equations discretization error Discussion and References eigenvalues eigenvectors Euler's method evaluated exact solution example Exercise Figure finite difference method formula Gauss–Seidel Gaussian elimination given grid points Hence Hessenberg Hessenberg matrix illconditioned initial conditions initialvalue problem interchange iterative methods linear equations linear system LU decomposition main diagonal multiplications n x n Newton iterates Newton's method nonzero nonlinear nonsingular norm obtain operation count ordinary differential equations orthogonal orthogonal matrix partial differential equations permutation matrix piecewise polynomial of degree positive definite QR method quadratic rate of convergence requires roots rounding error RungeKutta method satisfies scientific computing secondorder Show stability step Supplementary Discussion symmetric system of equations Theorem triangular tridiagonal matrix value problem variables vector verify yk+1