## Numerical Solution of Ordinary Differential Equations: For Classical, Relativistic and Nano SystemsThis work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language. Each chapter is rounded off with exercises. |

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### Contents

RungeKutta Methods | 11 |

The Method of Taylor Expansions | 37 |

Completely Conservative Covariant Numerical Methodology | 77 |

Copyright | |

9 other sections not shown

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Numerical Solution of Ordinary Differential Equations: For Classical ... Donald Greenspan Limited preview - 2008 |

### Common terms and phrases

2006 WILEY-VCH Verlag 2200 point trajectory algorithm assume asymptotically stable axis boundary value problem coefficients Compare your results conditions of Theorem Consider constant covariant Cusped path decimal places defined difference equation Donald Greenspan Copyright Equations for Classical Euler's method exact solution Example find the numerical follows given hP(x implies initial data initial value problem interior grid point KGaA Kutta's formulas lab frame Lemma Lorentz transformation main diagonal main diagonal elements mildly nonlinear system molecular molecules motion N-body problem Nano Systems Newton–Lieberstein method Newton's method Newtonian numerical method numerical solution º º Ordinary Differential Equations Orik particle path of Pi point xi Relativistic and Nano rocket frame showing 2200 points shown in Figure ſº Solution of Ordinary solve special relativity speed of light Step Taylor expansion Theorem 7.1 tridiagonal system unique solution unstable valid vector velocity Weinheim ISBN XY plane yields