Index

0-stability, 137

2h Backward Euler Method, 168

2h trapezoidal method, 168

P th-order accurate, 136

r-stage one-step methods, 134

y-midpoint method, 169

A-stable, 162, 292

absolute stability, 137

Adams-Bashforth, 283

Adams-Moulton, 283

advection equation, 197

aliasing, 210

amplification factor, 140, 213, 220

analytic ODE, 31

analytical solution, 141

Asymptotic Stability Theorem, 47

asymptotically stable, 47

autonomous, 12

backward difference formula, 282

Backward Euler Method, 165

Banach Contraction Principle, 233,

235, 237

Banach space, 226

Butcher tableau, 266

butterfly, 25

Calculus of Variations, 63, 68

canonical coordinates, 64

canonical lifting, 65

Cartesian, 248

CFL condition, 200

chaos, 25

characteristic polynomial, 157, 290

characteristics, 199, 211

Classical Fourth-Order

Runge-Kutta (Classical RK4),

176

clock, 22

closed orbit, 20

closed system, 91

configuration space, 96

conjugate momentum, 73

Conservation Laws, 73

Conservation of Angular

Momentum, 120

Conservation of Energy, 74

Conservation of Linear Momentum,

118

consistent, 138, 286

constant method, 295

constant of the motion, 33

continuity of solutions w.r.t. V , 24

continuity with respect to initial

conditions, 22

continuous extension, 216, 221

convergent, 136

convergent algorithm, 18

Coriolis force, 104

corrector, 295

311