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
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