From the Book - Regular Print - Second edition.
1 Introduction and Programming Preliminaries 1 --
1.2 Running programs 1 --
1.4 External Fortran subprogram libraries 2 --
1.5 A simple Fortran program 4 --
1.6 Some simple Fortran constructs 7 --
1.7 Intrinsic functions 7 --
1.8 User-supplied functions and subroutines 8 --
1.9 Errors and accuracy 9 --
1.10 Graphical output 12 --
2 Linear Algebraic Equations 15 --
2.2 Gaussian elimination 15 --
2.3 Equation solution using factorization 20 --
2.4 Equations with a symmetrical coefficient matrix 25 --
2.5 Banded equations 33 --
2.6 Compact storage for variable bandwidths 35 --
2.8 Equations with prescribed solutions 42 --
2.9 Iterative methods 46 --
2.10 Gradient methods 61 --
2.11 Unsymmetrical systems 68 --
2.12 Preconditioning 72 --
2.13 Comparison of direct and iterative methods 81 --
3 Nonlinear Equations 89 --
3.2 Iterative substitution 91 --
3.3 Multiple roots and other difficulties 94 --
3.4 Interpolation methods 97 --
3.5 Extrapolation methods 103 --
3.6 Acceleration of convergence 112 --
3.7 Systems of nonlinear equations 112 --
4 Eigenvalue Equations 131 --
4.2 Vector iteration 136 --
4.3 Intermediate eigenvalues by deflation 148 --
4.4 Generalized eigenvalue problem [K]{x} = [lambda M]{x} 150 --
4.5 Transformation methods 158 --
4.6 Characteristic polynomial methods 180 --
5 Interpolation and Curve Fitting 193 --
5.2 Interpolating polynomials 193 --
5.3 Interpolation using cubic spline functions 207 --
5.4 Numerical differentiation 214 --
6 Numerical Integration 245 --
6.2 Newton-Cotes rules 247 --
6.3 Gauss-Legendre rules 265 --
6.4 Adaptive integration rules 278 --
6.5 Special integration rules 284 --
6.6 Multiple integrals 292 --
7 Numerical Solution of Ordinary Differential Equations 317 --
7.2 Definitions and types of ODE 317 --
7.3 Initial value problems 319 --
7.4 Boundary value problems 362 --
8 Introduction to Partial Differential Equations 393 --
8.2 Definitions and types of PDE 393 --
8.3 First order equations 394 --
8.4 Second order equations 399 --
8.5 Finite difference method 401 --
8.6 Finite element method 430 --
A Descriptions of Library Subprograms 445 --
B Fortran 95 Listings of Library Subprograms 447 --
C References and Additional Reading 469.