Index 313 Newton’s equations, 86 Newton’s Laws of Motion, 92 Newton’s Method, 160 No Bounded Escape Theorem, 14 nonautonomous, 12 norm, 226 normed vector space, 226 numerical methods, 133 orbit, 14 order of accuracy, 136 ordinary differential equation (ODE), 1 parabolic, 197 partial differential equation (PDE), 1 pendulum, 113 Pendulum Equation, 111 period, 20 periodic solution, 20 Pierre Simon de Laplace, 25 polynomial accuracy, 142 potential function, 106 precession, 121 predator-prey model, 59 predictor, 294 predictor-corrector, 163 prerequisites, 2 prime period, 21 propagator, 49 Ralston’s Method, 279 region of absolute stability, 148 relative stability, 299 residual, 216, 221 residual error, 214 resonant, 56 rest point, 20 Rikitake Two-Disk Dynamo, 29 root condition, 172 rooted trees, 267 Runge-Kutta, 134 Runge-Kutta expansion, 267 second-order ODE, 66 sensitive dependence on initial conditions, 27 singularity, 20 small oscillations about equilibrium, 126 smoke particle, 6 smoothness w.r.t. initial conditions, 23 smoothness w.r.t. parameters, 24 solution (of an IVP), 8 spectral method, 141 Spectral Theorem, 259 splitting method, 208 stability, 137 stable equilibrium, 47 stable subspace, 45 stationary point, 20 step-size, 134 stiff, 139 Straightening Theorem, 252 Strang splitting, 209 strange attractor, 27, 31 strong root condition, 299 successive approximations, 39 Taylor Methods, 263 Theorem on Smoothness w.r.t. Initial Conditions, 258 time-steps, 134 total energy function, 74 trapezoidal method, 159 Uniqueness Theorem, 8 unstable subspace, 45 variation of parameters, 52 variational equation, 257 vector field, 5 visual aids, 3 Volterra-Lotka equations, 59 weak stability, 299 Web Companion, 3 well-posed, 26

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