Page - 322 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

322 Index Programming, 2 game, 75 Prompt, 39 Pseudo-random numbers, 54 py.test, 155 Python, 2 documentation, 34 installation,4 interpreter, 6 shell, 39 zero-based indexing, 47 randint, 54 random, 54 random (function), 72 Random numbers, 54 vectorized, 54 Random walk (2D), 72 range (function), 63 Rate ofconvergence, 152, 192 Read (from file), 122 Readable code, 34 Refactor a program, 275 Reserved words, 41 Resonance, 262 return, 79 value, 85 RK2,246 Rootfinding, 176 Rounding error, 45, 154, 169 Runge-Kutta-Fehlberg, 252 Runge-Kutta, 2nd-order method, 246 Runge-Kutta, 3rd order, 279 Sage (symbolic package), 113 Scalar ODE,232 Scaling, 261, 298 Scheme, 183 Script (and scripting), 3 secant method, 188 Second-order ODE rewritten as two first-order ODEs, 241 2nd-order Runge-Kutta method, 246 Seed, 54, 167 fixing the,54 Semi-colon, 8 Semi-implicitEuler method, 245 Simplependulum, 241 Simpson’s rule, 145 Simulation,4 Single-step methods, 280 SIR model, 225 Source term, 288 split (function), 122 Spring damping of, 239, 257 linear, 260 nonlinear, 257 oscillations,239 Spyder, 4 Stabilitycriterion, 297 Statements, 7 Stop program (Ctrl+c), 67 str type,42 Symbolic computations, 111 operations, 111 simplifications, 111 SymPy, 111 Syntax, 2 sys.exit, 110, 119, 185, 188, 191 System of ODEs, 232 Taylor series, 277 Test block, 119 Test function, 155 Testing, 34 Testing procedures, 151 Text editor, 11 TextWrangler, 11, 314 ThetaRule, 306 Transpose (of matrix), 52 Trapezoidal rule, 134 Tridiagonal matrix, 303 Triple integral midpoint, 161 True, 46 try-except, 106, 186 Tuple, 32, 103 Type conversion, 42 float, 42 int,42 str, 42 uniform, 54 Unit tests, 150 Unstable solutions, 297 User, 32 Validation,34 Variable, 7 assignment, 7, 41 delete,36 global, 83 local, 83 name, 41 Vector, 52 vectorization, 146, 299 vector ODE,232 Verification, 34 Verlet integration, 267 Vim,11,314