java实现Romberg算法(附完整源码)
时间: 2023-12-06 16:22:55 浏览: 44
下面是Java实现Romberg算法的完整源码:
```java
import java.util.Scanner;
public class RombergAlgorithm {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.print("Enter the lower limit of integration: ");
double a = sc.nextDouble();
System.out.print("Enter the upper limit of integration: ");
double b = sc.nextDouble();
System.out.print("Enter the number of sub-intervals: ");
int n = sc.nextInt();
double[][] R = new double[n + 1][n + 1];
// Compute R[0][0]
double h = b - a;
R[0][0] = (h / 2) * (f(a) + f(b));
// Compute R[i][0] for i = 1, 2, ..., n
for (int i = 1; i <= n; i++) {
h /= 2;
double sum = 0;
for (int j = 1; j <= Math.pow(2, i - 1); j++) {
sum += f(a + (2 * j - 1) * h);
}
R[i][0] = 0.5 * R[i - 1][0] + sum * h;
}
// Compute R[i][j] for i = j, j + 1, ..., n
for (int j = 1; j <= n; j++) {
for (int i = j; i <= n; i++) {
R[i][j] = (Math.pow(4, j) * R[i][j - 1] - R[i - 1][j - 1]) / (Math.pow(4, j) - 1);
}
}
// Print R table
System.out.println("\nR Table:");
for (int i = 0; i <= n; i++) {
for (int j = 0; j <= i; j++) {
System.out.printf("%.6f\t", R[i][j]);
}
System.out.println();
}
// Print result
System.out.printf("\nIntegral value: %.6f", R[n][n]);
}
// Define the function to be integrated
public static double f(double x) {
return Math.sin(x) / x;
}
}
```
代码中使用了一个二维数组R来存储Romberg表格中的数值,其中R[i][j]表示用2^j个子区间计算第i次迭代的积分估计值。
程序首先读取积分区间和子区间个数,并计算出R[0][0]的值。然后,使用递推公式计算R[i][0](其中i为1到n),再利用递推公式计算R[i][j](其中i为j到n,j为1到n)。
最后,程序输出Romberg表格和最终积分估计值。
以上是Java实现Romberg算法的完整源码,希望能对你有所帮助。