Preface to the Second Edition | p. ix |

Preface to the First Edition | p. xi |

Interpolation | p. 1 |

Lagrange Polynomial Interpolation | p. 1 |

Cubic Spline Interpolation | p. 4 |

Exercises | p. 8 |

Further Reading | p. 12 |

Numerical Differentiation - Finite Differences | p. 13 |

Construction of Difference Formulas Using Taylor Series | p. 13 |

A General Technique for Construction of Finite Difference Schemes | p. 15 |

An Alternative Measure for the Accuracy of Finite Differences | p. 17 |

Padé Approximations | p. 20 |

Non-Uniform Grids | p. 23 |

Exercises | p. 25 |

Further Reading | p. 29 |

Numerical Integration | p. 30 |

Trapezoidal and Simpson's Rules | p. 30 |

Error Analysis | p. 31 |

Trapezoidal Rule with End-Correction | p. 34 |

Romberg Integration and Richardson Extrapolation | p. 35 |

Adaptive Quadrature | p. 37 |

Gauss Quadrature | p. 40 |

Exercises | p. 44 |

Further Reading | p. 47 |

Numerical Solution of Ordinary Differential Equations | p. 48 |

Initial Value Problems | p. 48 |

Numerical Stability | p. 50 |

Stability Analysis for the Euler Method | p. 52 |

Implicit or Backward Euler | p. 55 |

Numerical Accuracy Revisited | p. 56 |

Trapezoidal Method | p. 58 |

Linearization for Implicit Methods | p. 62 |

Runge-Kutta Methods | p. 64 |

Multi-Step Methods | p. 70 |

System of First-Order Ordinary Differential Equations | p. 74 |

Boundary Value Problems | p. 78 |

Shooting Method | p. 79 |

Direct Methods | p. 82 |

Exercises | p. 84 |

Further Reading | p. 100 |

Numerical Solution of Partial Differential Equations | p. 101 |

Semi-Discretization | p. 102 |

von Neumann Stability Analysis | p. 109 |

Modified Wavenumber Analysis | p. 111 |

Implicit Time Advancement | p. 116 |

Accuracy via Modified Equation | p. ll9 |

Du Fort-Frankel Method: An Inconsistent Scheme | p. 121 |

Multi-Dimensions | p. 124 |

Implicit Methods in Higher Dimensions | p. 126 |

Approximate Factorization | p. 128 |

Stability of the Factored Scheme | p. 133 |

Alternating Direction Implicit Methods | p. 134 |

Mixed and Fractional Step Methods | p. 136 |

Elliptic Partial Differential Equations | p. 137 |

Iterative Solution Methods | p. 140 |

The Point Jacobi Method | p. l41 |

Gauss-Seidel Method | p. 143 |

Successive Over Relaxation Scheme | p. 144 |

Multigrid Acceleration | p. 147 |

Exercises | p. 154 |

Further Reading | p. 166 |

Discrete Transform Methods | p. 167 |

Fourier Series | p. 167 |

Discrete Fourier Series | p. 168 |

Fast Fourier Transform | p. 169 |

Fourier Transform of a Real Function | p. 170 |

Discrete Fourier Series in Higher Dimensions | p. 172 |

Discrete Fourier Transform of a Product of Two Functions | p. 173 |

Discrete Sine and Cosine Transforms | p. 175 |

Applications of Discrete Fourier Series | p. 176 |

Direct Solution of Finite Differenced Elliptic Equations | p. 176 |

Differentiation of a Periodic Function Using Fourier Spectral Method | p. 180 |

Numerical Solution of Linear, Constant Coefficient Differential Equations with Periodic Boundary Conditions | p. 182 |

Matrix Operator for Fourier Spectral Numerical Differentiation | p. 185 |

Discrete Chebyshev Transform and Applications | p. 188 |

Numerical Differentiation Using Chebyshev Polynomials | p. 192 |

Quadrature Using Chebyshev Polynomials | p. 195 |

Matrix Form of Chebyshev Collocation Derivative | p. 196 |

Method of Weighted Residuals | p. 200 |

The Finite Element Method | p. 201 |

Application of the Finite Element Method to a Boundary Value Problem | p. 202 |

Comparison with Finite Difference Method | p. 207 |

Comparison with a Padé Scheme | p. 209 |

A Time-Dependent Problem | p. 210 |

Application to Complex Domains | p. 213 |

Constructing the Basis Functions | p. 215 |

Exercises | p. 221 |

Further Reading | p. 226 |

A Review of Linear Algebra | p. 227 |

Vectors, Matrices and Elementary Operations | p. 227 |

System of Linear Algebraic Equations | p. 230 |

Effects of Round-off Error | p. 230 |

Operations Counts | p. 231 |

Eigenvalues and Eigenvectors | p. 232 |

Index | p. 235 |

Table of Contents provided by Ingram. All Rights Reserved. |