子彈垂直向上射擊實驗, 子彈的終端速度為
f(x) = 1.15*10^-5*X^2 + 1.4*10^-5*X -1.962*10^-2
請使用 二分法 計算v的值 誤差=0.001
程式
// C program for implementation of Bisection Method for
// solving equations
#include <stdio.h>
#define EPSILON 0.001
// An example function whose solution is determined using
// Bisection Method. The function is x^3 - 4x + 2
double func(double x)
{
return 0.0000115*x*x +0.000014* pow(x,1.5) -0.01962;
}
// Prints root of func(x) with error of EPSILON
void bisection(double a, double b)
{
if (func(a) * func(b) >= 0)
{
printf("You have not assumed right a and b\n");
return;
}
double c = a;
while ((b-a) >= EPSILON)
{
// Find middle point
c = (a+b)/2;
// Check if middle point is root
if (func(c) == 0.0)
break;
// Decide the side to repeat the steps
else if (func(c)*func(a) < 0)
b = c;
else
a = c;
}
printf("The value of root is :%.6lf\n" ,c);
}
// Driver program to test above function
int main()
{
// Initial values assumed
double a =0.0, b =50.0 , x=a;
while ((b-x) >= -1.0)
{
printf("%0.1lf <---> %0.4lf\n",x,func(x));
x=x+1;
}
a =37.0;
b =38.0 ;
printf("\n%0.1lf to %0.1lf , the roots --> \n",a,b);
bisection(a, b);
return 0;
}
輸出畫面
0.0 <---> -0.0196
1.0 <---> -0.0196
2.0 <---> -0.0195
3.0 <---> -0.0194
4.0 <---> -0.0193
5.0 <---> -0.0192
6.0 <---> -0.0190
7.0 <---> -0.0188
8.0 <---> -0.0186
9.0 <---> -0.0183
10.0 <---> -0.0180
11.0 <---> -0.0177
12.0 <---> -0.0174
13.0 <---> -0.0170
14.0 <---> -0.0166
15.0 <---> -0.0162
16.0 <---> -0.0158
17.0 <---> -0.0153
18.0 <---> -0.0148
19.0 <---> -0.0143
20.0 <---> -0.0138
21.0 <---> -0.0132
22.0 <---> -0.0126
23.0 <---> -0.0120
24.0 <---> -0.0113
25.0 <---> -0.0107
26.0 <---> -0.0100
27.0 <---> -0.0093
28.0 <---> -0.0085
29.0 <---> -0.0078
30.0 <---> -0.0070
31.0 <---> -0.0062
32.0 <---> -0.0053
33.0 <---> -0.0044
34.0 <---> -0.0036
35.0 <---> -0.0026
36.0 <---> -0.0017
37.0 <---> -0.0007
38.0 <---> 0.0003
39.0 <---> 0.0013
40.0 <---> 0.0023
41.0 <---> 0.0034
42.0 <---> 0.0045
43.0 <---> 0.0056
44.0 <---> 0.0067
45.0 <---> 0.0079
46.0 <---> 0.0091
47.0 <---> 0.0103
48.0 <---> 0.0115
49.0 <---> 0.0128
50.0 <---> 0.0141
51.0 <---> 0.0154
37.0 to 38.0 , the roots -->
The value of root is :37.735352
...Program finished with exit code 0
Press ENTER to exit console.
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