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lwj
2025-06-14 11:40:57 +08:00
parent b509f51ceb
commit 852ee942ef
5 changed files with 15 additions and 9 deletions
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3
159-2.py
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@@ -1,6 +1,7 @@
import math import math
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
#把原函数换成题干的形式########################
def fx(x): def fx(x):
return math.exp(x)-math.sin(x) return math.exp(x)-math.sin(x)
@@ -25,7 +26,7 @@ def DrawGraph(a, b, stepper):
plt.show() plt.show()
return x, y return x, y
#把范围改成题干的形式#######################
if __name__ == "__main__": if __name__ == "__main__":
a = -2*math.pi a = -2*math.pi
b = math.pi b = math.pi

7
159-5.py
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@@ -1,6 +1,6 @@
import math import math
#原函数和导数改成题干的形式#####################
def f1(x): def f1(x):
return x**2 + 10*math.cos(x) return x**2 + 10*math.cos(x)
@@ -17,12 +17,14 @@ def df2(x):
# 牛顿方法求解方程 # 牛顿方法求解方程
def NewtonSolve(fx, dfx, x0, err, N0): def NewtonSolve(fx, dfx, x0, err, N0):
count = 0 count = 0
print(f"k={count}, x0={x0}")
x1 = x0 + 1 + err x1 = x0 + 1 + err
while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题 while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
if abs(dfx(x1)) < 1e-10: if abs(dfx(x1)) < 1e-10:
return None, 0 return None, 0
x1 = x0 - fx(x0) / dfx(x0) x1 = x0 - fx(x0) / dfx(x0)
count += 1 count += 1
print(f"k={count}, x{count}={x1},x1-x0={abs(x1-x0)}")
if count > N0: if count > N0:
return None, -1 return None, -1
x0 = x1 x0 = x1
@@ -41,6 +43,7 @@ if __name__ == "__main__":
err = 1e-5 err = 1e-5
N0 = 100 N0 = 100
#把初始值换成题干形式###############
x0 = 1.6 x0 = 1.6
result,status = NewtonSolve(f1, df1, x0, err,N0) result,status = NewtonSolve(f1, df1, x0, err,N0)
if status == 1: if status == 1:
@@ -51,7 +54,7 @@ if __name__ == "__main__":
print("f1导数为0，无法收敛") print("f1导数为0，无法收敛")
x0 = FindRootZone(f2, -5, 5, 0.01) x0 = FindRootZone(f2, -5, 5, 0.01) # 查找f2的根区间与步长
result, status = NewtonSolve(f2, df2, x0, err,N0) result, status = NewtonSolve(f2, df2, x0, err,N0)
if status == 1: if status == 1:
print(f"f2收敛 解为: {result}") print(f"f2收敛 解为: {result}")

6
159-6.py
View File

@@ -1,6 +1,6 @@
import math import math
#把函数改成题干的形式#####################
def f(x): def f(x):
return x**2 - 30 return x**2 - 30
@@ -10,12 +10,14 @@ def df(x):
# 牛顿方法求解方程 # 牛顿方法求解方程
def NewtonSolve(fx, dfx, x0, err, N0): def NewtonSolve(fx, dfx, x0, err, N0):
count = 0 count = 0
print(f"k={count}, x0={x0}")
x1 = x0 + 1 + err x1 = x0 + 1 + err
while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题 while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
if abs(dfx(x1)) < 1e-10: if abs(dfx(x1)) < 1e-10:
return None, 0 return None, 0
x1 = x0 - fx(x0) / dfx(x0) x1 = x0 - fx(x0) / dfx(x0)
count += 1 count += 1
print(f"k={count}, x{count}={x1},x1-x0={abs(x1-x0)}")
if count > N0: if count > N0:
return None, -1 return None, -1
x0 = x1 x0 = x1
@@ -34,6 +36,6 @@ if __name__ == "__main__":
err = 1e-4 err = 1e-4
N0 = 100 N0 = 100
x0 = FindRootZone(f, 5, 6, 0.01) x0 = FindRootZone(f, 5, 6, 0.1) # 查找f的根的区间与步长，改成题干对应的范围
result,status = NewtonSolve(f, df, x0, err,N0) result,status = NewtonSolve(f, df, x0, err,N0)
print(f"sqrt(30) = {result:.3f}") print(f"sqrt(30) = {result:.3f}")

4
160-11.py
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@@ -17,11 +17,11 @@ def SecantSolve(fx, x0, x1, err=1e-10, N0=100):
x1 = x2 x1 = x2
return x2,1 return x2,1
#把精度要求改成题干要求的##########################
if __name__ == "__main__": if __name__ == "__main__":
err = 1e-5 err = 1e-5
N0 = 100 N0 = 100
##把初始函数和初始值改成题干要求的##########################
x0 = 0.3 x0 = 0.3
x1 = 0.4 x1 = 0.4
fx = lambda x: x**4 - 3*x + 1 fx = lambda x: x**4 - 3*x + 1

4
160-12.py
View File

@@ -45,12 +45,12 @@ def MullerSolve(fx,x0,x1,x2,err1,err2,N):
f2 = f3 f2 = f3
q = h1 q = h1
#精度要求#########################（152页）
if __name__ == "__main__": if __name__ == "__main__":
err1 = 1e-5 err1 = 1e-5
err2 = 1e-5 err2 = 1e-5
N = 100 N = 100
##把初始函数和初始值改成题干要求的##########################
x0 = 0.3 x0 = 0.3
x1 = 0.5 x1 = 0.5
x2 = 0.4 x2 = 0.4