def solver(x, ys, step, system: System, table: ButcherTable, end, order,
error):
def take_doublestep(_x, _ys, _step):
_ys += np.array(correction(_x, _ys, system, _step, table))
_x += _step
_ys += np.array(correction(_x, _ys, system, _step, table))
return _ys
while True:
if step + x >= end:
step = end - x
x = end
else:
x += step
next_ys = ys + correction(x, ys, system, step, table)
ys_doublestep = take_doublestep(x, ys, step / 2)
local_error = norm(ys_doublestep - next_ys) / (1 - 2**(-order))
if local_error > error * 2**order:
step /= 2
elif local_error > error:
step /= 2
ys = ys_doublestep
elif local_error > error / 2**(order + 1):
ys = next_ys
else:
step *= 2
ys = next_ys
if x >= end:
break
return ys
def _const_step_solver(x, ys, step, system: System, table: ButcherTable, end):
while True:
if step + x >= end:
step = end - x
x = end
else:
x += step
ys += correction(x, ys, system, step, table)
if x >= end:
break
return ys
def take_doublestep(_x, _ys, _step):
_ys += np.array(correction(_x, _ys, system, _step, table))
_x += _step
_ys += np.array(correction(_x, _ys, system, _step, table))
return _ys