|
115 | 115 | "cell_type": "code", |
116 | 116 | "collapsed": false, |
117 | 117 | "input": [ |
118 | | - "import numpy as np\n", |
| 118 | + "import numpy\n", |
119 | 119 | "import sympy" |
120 | 120 | ], |
121 | 121 | "language": "python", |
|
154 | 154 | "collapsed": false, |
155 | 155 | "input": [ |
156 | 156 | "x, nu, t = sympy.symbols('x nu t')\n", |
157 | | - "phi = sympy.exp(-(x-4*t)**2/(4*nu*(t+1))) + sympy.exp(-(x-4*t-2*np.pi)**2/(4*nu*(t+1)))\n", |
| 157 | + "phi = sympy.exp(-(x-4*t)**2/(4*nu*(t+1))) + sympy.exp(-(x-4*t-2*numpy.pi)**2/(4*nu*(t+1)))\n", |
158 | 158 | "phi" |
159 | 159 | ], |
160 | 160 | "language": "python", |
|
325 | 325 | "cell_type": "code", |
326 | 326 | "collapsed": false, |
327 | 327 | "input": [ |
328 | | - "import matplotlib.pyplot as plt\n", |
| 328 | + "from matplotlib import pyplot\n", |
329 | 329 | "%matplotlib inline\n", |
330 | 330 | "\n", |
331 | 331 | "###variable declarations\n", |
332 | 332 | "nx = 101\n", |
333 | 333 | "nt = 100\n", |
334 | | - "dx = 2*np.pi/(nx-1)\n", |
| 334 | + "dx = 2*numpy.pi/(nx-1)\n", |
335 | 335 | "nu = .07\n", |
336 | 336 | "dt = dx*nu\n", |
337 | 337 | "\n", |
338 | | - "x = np.linspace(0, 2*np.pi, nx)\n", |
339 | | - "#u = np.empty(nx)\n", |
340 | | - "un = np.empty(nx)\n", |
| 338 | + "x = numpy.linspace(0, 2*np.pi, nx)\n", |
| 339 | + "#u = numpy.empty(nx)\n", |
| 340 | + "un = numpy.empty(nx)\n", |
341 | 341 | "t = 0\n", |
342 | 342 | "\n", |
343 | | - "u = np.asarray([ufunc(t, x0, nu) for x0 in x])\n", |
| 343 | + "u = numpy.asarray([ufunc(t, x0, nu) for x0 in x])\n", |
344 | 344 | "u" |
345 | 345 | ], |
346 | 346 | "language": "python", |
|
380 | 380 | "cell_type": "code", |
381 | 381 | "collapsed": false, |
382 | 382 | "input": [ |
383 | | - "plt.figure(figsize=(11,7), dpi=100)\n", |
384 | | - "plt.plot(x,u, marker='o', lw=2)\n", |
385 | | - "plt.xlim([0,2*np.pi])\n", |
386 | | - "plt.ylim([0,10]);" |
| 383 | + "pyplot.figure(figsize=(11,7), dpi=100)\n", |
| 384 | + "pyplot.plot(x,u, marker='o', lw=2)\n", |
| 385 | + "pyplot.xlim([0,2*numpy.pi])\n", |
| 386 | + "pyplot.ylim([0,10]);" |
387 | 387 | ], |
388 | 388 | "language": "python", |
389 | 389 | "metadata": {}, |
|
438 | 438 | " u[-1] = un[-1] - un[-1] * dt/dx * (un[-1] - un[-2]) + nu*dt/dx**2*\\\n", |
439 | 439 | " (un[0]-2*un[-1]+un[-2])\n", |
440 | 440 | " \n", |
441 | | - "u_analytical = np.asarray([ufunc(nt*dt, xi, nu) for xi in x])" |
| 441 | + "u_analytical = numpy.asarray([ufunc(nt*dt, xi, nu) for xi in x])" |
442 | 442 | ], |
443 | 443 | "language": "python", |
444 | 444 | "metadata": {}, |
|
449 | 449 | "cell_type": "code", |
450 | 450 | "collapsed": false, |
451 | 451 | "input": [ |
452 | | - "plt.figure(figsize=(11,7), dpi=100)\n", |
453 | | - "plt.plot(x,u, marker='o', lw=2, label='Computational')\n", |
454 | | - "plt.plot(x, u_analytical, label='Analytical')\n", |
455 | | - "plt.xlim([0,2*np.pi])\n", |
456 | | - "plt.ylim([0,10])\n", |
457 | | - "plt.legend();" |
| 452 | + "pyplot.figure(figsize=(11,7), dpi=100)\n", |
| 453 | + "pyplot.plot(x,u, marker='o', lw=2, label='Computational')\n", |
| 454 | + "pyplot.plot(x, u_analytical, label='Analytical')\n", |
| 455 | + "pyplot.xlim([0,2*numpy.pi])\n", |
| 456 | + "pyplot.ylim([0,10])\n", |
| 457 | + "pyplot.legend();" |
458 | 458 | ], |
459 | 459 | "language": "python", |
460 | 460 | "metadata": {}, |
|
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