Preface to the Second Edition |
Preface to the First Edition |
Interpolation / 1: |
Lagrange Polynomial Interpolation / 1.1: |
Cubic Spline Interpolation / 1.2: |
Exercises |
Further Reading |
Numerical Differentiation - Finite Differences / 2: |
Construction of Difference Formulas Using Taylor Series / 2.1: |
A General Technique for Construction of Finite Difference Schemes / 2.2: |
An Alternative Measure for the Accuracy of Finite Differences / 2.3: |
Padé Approximations / 2.4: |
Non-Uniform Grids / 2.5: |
Numerical Integration / 3: |
Trapezoidal and Simpson's Rules / 3.1: |
Error Analysis / 3.2: |
Trapezoidal Rule with End-Correction / 3.3: |
Romberg Integration and Richardson Extrapolation / 3.4: |
Adaptive Quadrature / 3.5: |
Gauss Quadrature / 3.6: |
Numerical Solution of Ordinary Differential Equations / 4: |
Initial Value Problems / 4.1: |
Numerical Stability / 4.2: |
Stability Analysis for the Euler Method / 4.3: |
Implicit or Backward Euler / 4.4: |
Numerical Accuracy Revisited / 4.5: |
Trapezoidal Method / 4.6: |
Linearization for Implicit Methods / 4.7: |
Runge-Kutta Methods / 4.8: |
Multi-Step Methods / 4.9: |
System of First-Order Ordinary Differential Equations / 4.10: |
Boundary Value Problems / 4.11: |
Shooting Method / 4.11.1: |
Direct Methods / 4.11.2: |
Numerical Solution of Partial Differential Equations / 5: |
Semi-Discretization / 5.1: |
von Neumann Stability Analysis / 5.2: |
Modified Wavenumber Analysis / 5.3: |
Implicit Time Advancement / 5.4: |
Accuracy via Modified Equation / 5.5: |
Du Fort-Frankel Method: An Inconsistent Scheme / 5.6: |
Multi-Dimensions / 5.7: |
Implicit Methods in Higher Dimensions / 5.8: |
Approximate Factorization / 5.9: |
Stability of the Factored Scheme / 5.9.1: |
Alternating Direction Implicit Methods / 5.9.2: |
Mixed and Fractional Step Methods / 5.9.3: |
Elliptic Partial Differential Equations / 5.10: |
Iterative Solution Methods / 5.10.1: |
The Point Jacobi Method / 5.10.2: |
Gauss-Seidel Method / 5.10.3: |
Successive Over Relaxation Scheme / 5.10.4: |
Multigrid Acceleration / 5.10.5: |
Discrete Transform Methods / 6: |
Fourier Series / 6.1: |
Discrete Fourier Series / 6.1.1: |
Fast Fourier Transform / 6.1.2: |
Fourier Transform of a Real Function / 6.1.3: |
Discrete Fourier Series in Higher Dimensions / 6.1.4: |
Discrete Fourier Transform of a Product of Two Functions / 6.1.5: |
Discrete Sine and Cosine Transforms / 6.1.6: |
Applications of Discrete Fourier Series / 6.2: |
Direct Solution of Finite Differenced Elliptic Equations / 6.2.1: |
Differentiation of a Periodic Function Using Fourier Spectral Method / 6.2.2: |
Numerical Solution of Linear, Constant Coefficient Differential Equations with Periodic Boundary Conditions / 6.2.3: |
Matrix Operator for Fourier Spectral Numerical Differentiation / 6.3: |
Discrete Chebyshev Transform and Applications / 6.4: |
Numerical Differentiation Using Chebyshev Polynomials / 6.4.1: |
Quadrature Using Chebyshev Polynomials / 6.4.2: |
Matrix Form of Chebyshev Collocation Derivative / 6.4.3: |
Method of Weighted Residuals / 6.5: |
The Finite Element Method / 6.6: |
Application of the Finite Element Method to a Boundary Value Problem / 6.6.1: |
Comparison with Finite Difference Method / 6.6.2: |
Comparison with a Padé Scheme / 6.6.3: |
A Time-Dependent Problem / 6.6.4: |
Application to Complex Domains / 6.7: |
Constructing the Basis Functions / 6.7.1: |
A Review of Linear Algebra / A: |
Vectors, Matrices and Elementary Operations / A.1: |
System of Linear Algebraic Equations / A.2: |
Effects of Round-off Error / A.2.1: |
Operations Counts / A.3: |
Eigenvalues and Eigenvectors / A.4: |
Index |
Preface to the Second Edition |
Preface to the First Edition |
Interpolation / 1: |
Lagrange Polynomial Interpolation / 1.1: |
Cubic Spline Interpolation / 1.2: |
Exercises |