51 lines
1.2 KiB
Python
51 lines
1.2 KiB
Python
from typing import Callable
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class Edo:
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def __init__(self, function: Callable[[float], float]) -> None:
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self.F = function
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def euler(self, a: float, y: float, b: float, n: int = 10**6) -> float:
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dx = (b - a) / n
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def x(i):
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return a + i * dx
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for i in range(n):
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y = y + (self.F(x(i), y)) * dx
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return y
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def runge(self, a: float, y: float, b: float, n: int = 10**6) -> float:
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dx = (b - a) / n
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def x(i):
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return a + i * dx
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for i in range(n):
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y = y + (dx / 2) * (self.F(x(i), y) + self.F(x(i + 1), (y + (dx * self.F(x(i), y)))))
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return y
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def adams(self, a: float, y: float, b: float, n: int = None
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) -> float:
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if n is None:
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n = 10 ** 6
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dx = (b - a) / n
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def x(i):
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return a + i * dx
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for i in range(n):
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f0 = self.F(x(i), y)
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f1 = self.F(x(i + 1), y + dx * self.F(x(i) + (dx / 2), y + (dx / 2) * self.F(x(i), y)))
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f2 = self.F(x(i + 2), y + (dx / 2) * (3 * f1 - f0))
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y += (dx / 12) * (5 * f2 + 8 * f1 - f0)
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return y |