Chapter I. Classical Mathematical Theory I.1 Terminology I.2 The Oldest Differential Equations I.3 Elementary Integration Methods I.4 Linear Differential Equations I.5 Equations with Weak Singularities I.6 Systme of Equations I.7 A General Existence Theorem I.8 Existence Theory using Iteration Methods and Taylor Series I.9 Existence Theory for Systems of Equations I.10 Differential Inequalities I.11 Systems of Linear Differential Equations I.12 Systmes with Constant Coefficients I.13 Stability I.14 Derivatives with Respect ot Parameters and Initial Values I.15 boundary Value and Eigenvalue Problems I.16 Periodic Solutions, Limit Cycles, Strange Attractors Chapter II. Runge-Kutta and Extrapolation Methods II.1 The First Runge-Kutta Methods II.2 Order Conditions for Runge-Kutta Methods II.3 Error Estimation and Convergence for RK Methods II.4 Practical Error Estimation and Step Size Selection II.5 Explicit Runge-Kutta Methods of Higher Order II.6 Dense Output, Discontinuities, Derviatives II.7 Implicit Runge-Kutta Methods II.8 Asymptotic Expansion of the Golbal Error II.9 Extrapolation Methods II.10 Numerical Comparisons II.11 Parallel Methods II.12 Composition of B-Series II.13 Higher Derivative Methods II.14 Numerical Methods for Second Order Differential Equations II.15 P-Series for Partitioned Differential Equations II.16 Symplectic Integration Methods II.17 Delay Differential Equations Chapter III. Multistep Methods and General Linear Methods III.1 Classical Linear Multistep Formulas III.2 Local Error and Order Conditions III.3 Stability and the First Dahlquist Barrier III.4 Convergence of Multistep Methods III.5 Variable Step Size Multistep Muthods III.6 Nordisieck Methods III.7 Implementation and Numerical Comparisons III.8 General Linear Methods III.9 Asymptotic Expansion of the Global Error III.10 Multistep Methods for Second Order Differential Equations Appendix. Fortran Codes Bibliography Symbol Index Subject Index
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