public class Test {
public static void main(String[] args) {
double a, b, accuracy; //a为区间下限，b为区间上限，accuracy为精度
a = 0;//积分下界
b = 0.8; //积分上界
accuracy = 1e-8;//精度
double h; //步长
h = b - a;
double T1, T2; //T1：二分前的梯形法积分值；T2：二分后的梯形法积分值；
T1 = h / 2 * (1 + f(b));
T2 = 0;
int k = 1; //记录二分次数
System.out.println("T" +Math.pow(2, 0) +" = " +T1);
double S1 = 0, S2; //对T1与T2加权平均，得辛普森积分值
double C1=0, C2; //对S1与S2加权平均，得柯特斯积分值
double R1 = 0, R2; //对C1，C2加权平均，得龙贝格积分值
int flag = 1; //flag作为循环控制标志性变量
while (flag == 1){
double sum = 0; //各分点的函数值和
double x = a + h / 2; //分点值
while (x < b) //在区间上限范围内求各分点的函数值和
{
sum += f(x);
x += h;
}
T2 = T1 / 2 + h / 2 * sum; //计算梯形序列得下一个二分结果
System.out.println("T" +Math.pow(2, k) + " = " + T2 );
S2 = T2 + 1.0 / 3 * (T2 - T1); //线性组合外推值simpson
System.out.println("S"+Math.pow(2, k - 1) +" = " +S2);
if (k == 1) //至少外推2次得出S1，S2
{
k++;
h /= 2;
T1 = T2;
S1 = S2;
continue;
}
else
{
C2 = S2 + 1.0 / 15 * (S2 - S1); //线性组合外推值Cotes
System.out.println("C"+Math.pow(2, k - 2) +" = "+C2);
if (k == 2) //至少外推3次得出C1，C2
{
C1 = C2;
k++;
h /= 2;
T1 = T2;
S1 = S2;
continue;
}
else
{
R2 = C2 + 1.0 / 63 * (C2 - C1); //线性组合外推至Romberg
System.out.println("R" +Math.pow(2, k - 3) + " = " + R2 );
if (k == 3) //至少外推4次得出R1,R2
{
R1 = R2;
C1 = C2;
k++;
h /= 2;
T1 = T2;
S1 = S2;
continue;
}
else if (Math.abs(R2 - R1) >= accuracy) //精度仍然不符合要求，继续二分步长、继续外推
{
R1 = R2;
C1 = C2;
k = k + 1;
h = h / 2;
T1 = T2;
S1 = S2;
}
else //精度符合要求，修改flag为0，跳出while循环
{
flag = 0;
System.out.println("Romber算法求得数值积分结果为:" +R2 );
}
}
}
}
}
static double f(double x) //自定义被积函数
{
double result;
result = Math.exp(Math.pow(-x,2));
return result;
}
}
运行结果得：
