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Éamonn Murray
IntroToScientificComputing
Commits
d29ca9cd
Commit
d29ca9cd
authored
Dec 05, 2017
by
Éamonn Murray
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Fix some typos
parent
f455fb06
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Differential Equations.ipynb
...ds/08_Differential_Equations/Differential Equations.ipynb
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numerical_methods/08_Differential_Equations/Differential Equations.ipynb
View file @
d29ca9cd
...
...
@@ 639,8 +639,8 @@
" \n",
" Returns\n",
" \n",
" x
, v
: float, array\n",
" Position a
nd velocity a
t each timestep.\n",
" x : float, array\n",
" Position at each timestep.\n",
" '''\n",
" # Initialize an empty arrays that will store x at each timestep.\n",
" x = np.empty(nt)\n",
...
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@@ 781,7 +781,7 @@
},
"outputs": [],
"source": [
"# Find the trajectory using our
leapfrog
function for\n",
"# Find the trajectory using our
verlet
function for\n",
"# two different starting values.\n",
"xvals3 = verlet(accel_quartic, 0.01, 0.0, dt, nt)\n",
"xvals4 = verlet(accel_quartic, 0.75, 0.0, dt, nt)\n",
...
...
@@ 879,7 +879,7 @@
},
"outputs": [],
"source": [
"# Find the trajectory using our
leapfrog
function for\n",
"# Find the trajectory using our
velocityverlet
function for\n",
"# two different starting values.\n",
"xvals5 = velocityverlet(accel_quartic, 0.01, 0.0, dt, nt)\n",
"xvals6 = velocityverlet(accel_quartic, 0.75, 0.0, dt, nt)\n",
...
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@@ 923,7 +923,7 @@
"and e.g. a central difference for the second derivative:\n",
"\n",
"$$\n",
"f''(x) \\approx \\frac{f(x+h)2f(x)

f(xh)}{h^2}\n",
"f''(x) \\approx \\frac{f(x+h)2f(x)
+
f(xh)}{h^2}\n",
"$$\n",
"\n",
"Say we're trying to solve some PDE of function in position and time, such as the heat or diffusion equation in one dimension:\n",
...
...
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