def solve(self, diff: DifferentialEq, precision=4) -> Tuple[Function]:
'''
Returns tuple of (method-derived function, LTE function, GTE function)
'''
# getting result function and lte
result, lte, _ = self.__execute_method(
diff.f,
diff.solution,
diff.x_0,
diff.y_0,
diff.x_n,
diff.n,
precision=precision,
)
# calculate gte for all n from `n_start` to `n_end`
gte = Function()
for n in range(diff.n_start, diff.n_end + 1):
_, _, gte_values = self.__execute_method(
diff.f,
diff.solution,
diff.x_0,
diff.y_0,
diff.x_n,
n,
precision=precision,
)
gte.append(n, max(gte_values.Y))
return result, lte, gte
def __execute_method(self,
f,
y_solution_func,
x_0,
y_0,
x_n,
n,
precision=4) -> Tuple[Function]:
'''
Basically execute iteration method
'''
h = (x_n - x_0) / n
assert (h > 0, 'x_n should be greater than x_0')
logging.debug(
f"Solving eq with steps {h}. y_0: {y_0} x_n: {x_n}, x_0: {x_0}, n: {n}"
)
result_function = Function([], [])
lte_function = Function([], [])
gte_function = Function([], [])
x_i = x_0
y_i = y_0
LTE = 0
GTE = 0
for i in range(1, n + 2):
# add values to result functions
result_function.append(x_i, y_i)
lte_function.append(x_i, LTE)
gte_function.append(x_i, GTE)
# execute method
y_i = self.get_next_value(f, x_i, y_i, h)
# errors
LTE = abs(y_solution_func(x_i + h) - \
self.get_next_value(
f, x_i, y_solution_func(x_i), h
)
)
GTE = abs(y_solution_func(x_i + h) - y_i)
# step
x_i = round(x_0 + i * h, precision)
y_init = y_solution_func(x_i)
return (result_function, lte_function, gte_function)