Page - 224 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

224 7 Index rootfinding, 186 roundingerror,13, 14 Runge-Kutta, 2nd-ordermethod, 131 Runge-Kutta-Fehlberg, 137 S Sage (symbolicpackage), 25 savetxt, 44 scalarODE,116 scaling, 144,170 scheme, 96 script (andscripting),3 second-orderODErewrittenas twofirst-order ODEs,126 seed (randomgenerators), 87 simplependulum, 125 Simpson’s rule,68 simulation,3 SIRmodel, 110 source term,161 spring dampingof, 124,141 linear, 144 nonlinear, 141 oscillations,124 Spyder, 6 stabilitycriterion,170 stopprogram(Ctrl+c),41 str,13 symbolic computations, 23 operations, 23 simplifications,23 SymPy, 23 syntax, 2 sys.exit, 200 systemofODEs,116 T Taylor series,157 testblock, 62 test function, 72 testing,22 testingprocedures, 69 text editor, 6 TextWrangler, 6,212 theta rule, 179 title (plot),20 transpose (ofmatrix), 21 Trapezoidal rule,57 tridiagonalmatrix,177 triple integral midpoint, 81 True, 29 try-exception, 22 tuple, 23, 41 typeconversion, 13 automatic, 14 U unit tests,69 unstable solutions,170 V validation, 22 variable, 5 assignment, 13 delete, 25 float, 13 global, 34 int, 13 local, 34 name, 13 str, 13 type, 13 vector, 21 vectorODE,116 vectorization, 76, 172 verification, 22 Verlet integration, 150 Vim,6, 212 W WARNING,8 while loop, 40 WolframAlpha, 24 write (tofile), 43 X xlabel, 11 Y ylabel, 11 Z zeros, 17