List of Examples; Preface; 1. Introduction. Boundary Value Problems for Ordinary Differential Equations; Boundary Value Problems in Applications; 2. Review of Numerical Analysis and Mathematical Background. Errors in Computation; Numerical Linear Algebra; Nonlinear Equations; Polynomial Interpolation; Piecewise Polynomials, or Splines; Numerical Quadrature; Initial Value Ordinary Differential Equations; Differential Operators and Their Discretizations; 3. Theory of Ordinary Differential Equations. Existence and Uniqueness Results; Green's Functions; Stability of Initial Value Problems; Conditioning of Boundary Value Problems; 4. Initial Value Methods. Introduction. Shooting; Superposition and Reduced Superposition; Multiple Shooting for Linear Problems; Marching Techniques for Multiple Shooting; The Riccati Method; Nonlinear Problems; 5. Finite Difference Methods. Introduction; Consistency, Stability, and Convergence; Higher-Order One-Step Schemes; Collocation Theory; Acceleration Techniques; Higher-Order ODEs; Finite Element Methods; 6. Decoupling. Decomposition of Vectors; Decoupling of the ODE; Decoupling of One-Step Recursions; Practical Aspects of Consistency; Closure and Its Implications; 7. Solving Linear Equations. General Staircase Matrices and Condensation; Algorithms for the Separated BC Case; Stability for Block Methods; Decomposition in the Nonseparated BC Case; Solution in More General Cases; 8. Solving Nonlinear Equations. Improving the Local Convergence of Newton's Method; Reducing the Cost of the Newton Iteration; Finding a Good Initial Guess; Further Remarks on Discrete Nonlinear BVPS; 9. Mesh Selection. Introduction; Direct Methods; A Mesh Strategy for Collocation; Transformation Methods; General Considerations; 10. Singular Perturbations. Analytical Approaches; Numerical Approaches; Difference Methods; Initial Value Methods; 11. Special Topics. Reformulation of Problems in 'Standard' Form; Generalized ODEs and Differential Algebraic Equations; Eigenvalue Problems; BVPs with Singularities; Infinite Intervals; Path Following, Singular Points and Bifurcation; Highly Oscillatory Solutions; Functional Differential Equations; Method of Lines for PDEs; Multipoint Problems; On Code Design and Comparison; Appendix A. A Multiple Shooting Code; Appendix B. A Collocation Code; References; Bibliography; Index.
