Contents ix 15.6 Confidence Limits on Estimated Model Parameters 689 15.7 Robust Estimation 699 16 Integration of Ordinary Differential Equations 707 16.0 Introduction 707 16.1 Runge-Kutta Method 710 16.2 Adaptive Stepsize Control for Runge-Kutta 714 16.3 Modified Midpoint Method 722 16.4 Richardson Extrapolation and the Bulirsch-Stoer Method 724 16.5 Second-Order Conservative Equations 732 16.6 Stiff Sets of Equations 734 16.7 Multistep,Multivalue,and Predictor-Corrector Methods 747 虽 from NUMERICAL RECIPES IN C: 19881992 17 Two Point Boundary Value Problems 753 17.0 Introduction 753 17.1 The Shooting Method 757 17.2 Shooting to a Fitting Point 760 17.3 Relaxation Methods 762 17.4 A Worked Example:Spheroidal Harmonics 772 (North America 州bMe se users to make one paper THE 17.5 Automated Allocation of Mesh Points 783 17.6 Handling Internal Boundary Conditions or Singular Points 784 9 Programs 18 Integral Equations and Inverse Theory 788 strictly proh 18.0 Introduction 788 18.1 Fredholm Equations of the Second Kind 791 18.2 Volterra Equations 794 18.3 Integral Equations with Singular Kernels 797 18.4 Inverse Problems and the Use of A Priori Information 804 18.5 Linear Regularization Methods 808 18.6 Backus-Gilbert Method 815 18.7 Maximum Entropy Image Restoration 818 1988-1992 by Numerical Recipes ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) 19 Partial Differential Equations 827 19.0 Introduction 827 19.1 Flux-Conservative Initial Value Problems 834 (outside 19.2 Diffusive Initial Value Problems 847 19.3 Initial Value Problems in Multidimensions 853 North Software. 19.4 Fourier and Cyclic Reduction Methods for Boundary Value Problems 857 19.5 Relaxation Methods for Boundary Value Problems 863 19.6 Multigrid Methods for Boundary Value Problems 871 20 Less-Numerical Algorithms 889 20.0 Introduction 889 20.1 Diagnosing Machine Parameters 889 20.2 Gray Codes 894Contents ix Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). 15.6 Confidence Limits on Estimated Model Parameters 689 15.7 Robust Estimation 699 16 Integration of Ordinary Differential Equations 707 16.0 Introduction 707 16.1 Runge-Kutta Method 710 16.2 Adaptive Stepsize Control for Runge-Kutta 714 16.3 Modified Midpoint Method 722 16.4 Richardson Extrapolation and the Bulirsch-Stoer Method 724 16.5 Second-Order Conservative Equations 732 16.6 Stiff Sets of Equations 734 16.7 Multistep, Multivalue, and Predictor-Corrector Methods 747 17 Two Point Boundary Value Problems 753 17.0 Introduction 753 17.1 The Shooting Method 757 17.2 Shooting to a Fitting Point 760 17.3 Relaxation Methods 762 17.4 A Worked Example: Spheroidal Harmonics 772 17.5 Automated Allocation of Mesh Points 783 17.6 Handling Internal Boundary Conditions or Singular Points 784 18 Integral Equations and Inverse Theory 788 18.0 Introduction 788 18.1 Fredholm Equations of the Second Kind 791 18.2 Volterra Equations 794 18.3 Integral Equations with Singular Kernels 797 18.4 Inverse Problems and the Use of A Priori Information 804 18.5 Linear Regularization Methods 808 18.6 Backus-Gilbert Method 815 18.7 Maximum Entropy Image Restoration 818 19 Partial Differential Equations 827 19.0 Introduction 827 19.1 Flux-Conservative Initial Value Problems 834 19.2 Diffusive Initial Value Problems 847 19.3 Initial Value Problems in Multidimensions 853 19.4 Fourier and Cyclic Reduction Methods for Boundary Value Problems 857 19.5 Relaxation Methods for Boundary Value Problems 863 19.6 Multigrid Methods for Boundary Value Problems 871 20 Less-Numerical Algorithms 889 20.0 Introduction 889 20.1 Diagnosing Machine Parameters 889 20.2 Gray Codes 894