┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.1, Release Date: 2023-08-20                    │
│ Using Python 3.10.12. Type "help()" for help.                      │
└────────────────────────────────────────────────────────────────────┘
sage: %colors nocolor
sage:
sage: def get_soln(y0, yp0, t0, tmax, deltat):
....:     soln = {t0:y0}
....:     y = y0
....:     t = t0
....:     yp = yp0
....:     while t < tmax:
....:         new_t = t + deltat
....:         new_y = y + yp * deltat
....:         new_yp = yp + F(y,yp,t) * deltat
....:         t = new_t
....:         y = new_y
....:         yp = new_yp
....:         soln[t] = y
....:     return soln
sage:
sage:
sage:
sage:
sage:
sage:
sage: def F(y,yp,t):
....:     to_ret = -0.1*yp - y + cos(2.0*t)
....:     return to_ret
....:
sage: time soln = get_soln(1,0,0,10,0.01)
CPU times: user 6.04 ms, sys: 4 µs, total: 6.05 ms
Wall time: 6.02 ms
sage:
sage: points( soln.items(), dpi=400, size=1)
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: time soln = get_soln(1,0,0,100,0.01)

CPU times: user 153 ms, sys: 3.98 ms, total: 157 ms
Wall time: 156 ms
sage:
sage: points( soln.items(), dpi=400, size=1)
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: time soln = get_soln(1,0,0,1000,0.01)
CPU times: user 1.04 s, sys: 27 ms, total: 1.07 s
Wall time: 1.07 s
sage: points( soln.items(), dpi=400, size=1)
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: soln = get_soln(1,0,0,1000,0.01)
sage: time soln = get_soln(1,0,0,1000,0.01)
CPU times: user 846 ms, sys: 12 ms, total: 858 ms
Wall time: 857 ms
sage:
sage:
sage:
sage: sorted(list(soln.items()))[:10]
[(0, 1),
 (0.0100000000000000, 1.00000000000000),
 (0.0200000000000000, 1.00000000000000),
 (0.0300000000000000, 0.999999980000667),
 (0.0400000000000000, 0.999999880031999),
 (0.0500000000000000, 0.999999600219293),
 (0.0600000000000000, 0.999999000869027),
 (0.0700000000000000, 0.999997902574617),
 (0.0800000000000000, 0.999996086342000),
 (0.0900000000000000, 0.999993293734980)]
sage: sorted(list(soln.items()))[:1000:100]
[(0, 1),
 (1.00000000000000, 0.866605484524718),
 (2.00000000000000, -0.269918822354881),
 (2.99999999999998, -1.47123448297629),
 (3.99999999999996, -0.689685392749432),
 (4.99999999999994, 0.544120597317060),
 (5.99999999999992, 0.680238891382552),
 (6.99999999999990, 0.720228312181525),
 (7.99999999999987, 0.208365812658922),
 (8.99999999999985, -1.02745962234716)]
sage: