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Solving ordinary differential equations Book

Solving ordinary differential equations
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  • Solving ordinary differential equations
  • Written by author G. Wanner
  • Published by Berlin ; Springer-Verlag, 1993-, 1993/09/01
Buy Digital  USD$131.75

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Ch. I Classical Mathematical Theory
I.1 Terminology 2
I.2 The Oldest Differential Equations 4
I.3 Elementary Integration Methods 12
I.4 Linear Differential Equations 16
I.5 Equations with Weak Singularities 20
I.6 Systems of Equations 26
I.7 A General Existence Theorem 35
I.8 Existence Theory using Iteration Methods and Taylor Series 44
I.9 Existence Theory for Systems of Equations 51
I.10 Differential Inequalities 56
I.11 Systems of Linear Differential Equations 64
I.12 Systems with Constant Coefficients 69
I.13 Stability 80
I.14 Derivatives with Respect to Parameters and Initial Values 92
I.15 Boundary Value and Eigenvalue Problems 105
I.16 Periodic Solutions, Limit Cycles, Strange Attractors 111
Ch. II Runge-Kutta and Extrapolation Methods
II.1 The First Runge-Kutta Methods 132
II.2 Order Conditions for Runge-Kutta Methods 143
II.3 Error Estimation and Convergence for RK Methods 156
II.4 Practical Error Estimation and Step Size Selection 164
II.5 Explicit Runge-Kutta Methods of Higher Order 173
II.6 Dense Output, Discontinuities, Derivatives 188
II.7 Implicit Runge-Kutta Methods 204
II.8 Asymptotic Expansion of the Global Error 216
II.9 Extrapolation Methods 224
II.10 Numerical Comparisons 244
II.11 Parallel Methods 257
II.12 Composition of B-Series 264
II.13 Higher Derivative Methods 274
II.14 Numerical Methods for Second Order Differential Equations 283
II.15 P-Series for Partitioned Differential Equations 302
II.16 Symplectic Integration Methods 312
II.17 Delay Differential Equations 339
Ch. III Multistep Methods and General Linear Methods
III.1 Classical Linear Multistep Formulas 356
III.2 Local Error and Order Conditions 368
III.3 Stability and the First Dahlquist Barrier 378
III.4 Convergence of Multistep Methods 391
III.5 Variable Step Size Multistep Methods 397
III.6 Nordsieck Methods 410
III.7 Implementation and Numerical Comparisons 421
III.8 General Linear Methods 430
III.9 Asymptotic Expansion of the Global Error 448
III.10 Multistep Methods for Second Order Differential Equations 461
Appendix. Fortran Codes 475
Bibliography 491
Symbol Index 521
Subject Index 523


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