四阶龙格库塔 步长求解步长h怎么确定?选取多少结果才比较精确?
1个回答
假设求解初值问题：
y'=y-2x/y (0
y(0)=1
设步长h=0.2,从x=0直到x=1用四阶龙格库塔法：
Private Sub Form_click()
Dim x As Single, y As Single
Dim k1 As Single, k2 As Single, k3 As Single, k4 As Single
Dim y1 As Single, y2 As Single, y3 As Single, y4 As Single
x = 0
y = 1
h = 0.2
For i = 0 To 1 Step 0.2
k1 = f(x, y)
y1 = y + h / 2 * k1
x = x + h / 2
k2 = f(x, y1)
y2 = y + h / 2 * k2
k3 = f(x, y2)
y3 = y + h * k3
x = x + h / 2
k4 = f(x, y3)
y = y + h / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
Print "x="; x; " y="; y
Next
End Sub
Private Function f(a As Single, b As Single) As Single
f = b - 2 * a / b
End Function
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