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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