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法律研究C++ 程式計算二重積分
我們給定變數 x 的下限、變數 x 的上限、變數 y 的下限、變數 y 的上限、對應 x 的步長、對應 y 的步長，任務是生成二重積分並顯示結果。
示例
Input-: steps for x = 1.2 steps for y = 0.54 lower limit of x = 1.3 upper limit of x = 2.1 lower limit of y = 1.0 upper limit for y = 2.1 Output-: double integration is : 2.1
**下面程式中使用的方法如下** −
- 輸入 x 和 y 的上限和下限，然後輸入 x 和 y 的步長
- 我們用於計算 x 和 y 的二重積分的方法是辛普森 1/3 方法
- 在繼續執行之前，生成以下表格
- 針對第一積分將辛普森 1/3 規則應用於每行，然後重複兩次以進行二重積分
- 列印結果
演算法
Start Step 1-> declare function to calculate power for integration float fun(float x, float y) return pow(pow(x, 4) + pow(y, 5), 0.5) Step 2-> declare function to find the double integral value float doubleIntegral(float step_x, float step_y, float lower_x, float upper_x, float lower_y, float upper_y) Declare int n1, n2 Declare float arr[50][50], arr_2[50], result set n1 = (upper_x - lower_x) / step_x + 1 set n2 = (upper_y - lower_y) / step_y + 1 Loop For int i = 0 and i < n1 and ++i Loop For int j = 0 and j < n2 and ++j set arr[i][j] = fun(lower_x + i * step_x, lower_y + j * step_y) End End Loop For int i = 0 and i < n1 and ++i set arr_2[i] = 0 Loop For int j = 0 and j < n2 and ++j IF (j == 0 || j == n2 - 1) Set arr_2[i] += arr[i][j] End Else IF (j % 2 == 0) Set arr_2[i] += 2 * arr[i][j] End Else set arr_2[i] += 4 * arr[i][j] End set arr_2[i] *= (step_y / 3) End set result = 0 Loop For int i = 0 and i < n1 and ++i IF (i == 0 || i == n1 - 1) set result += arr_2[i] End Else IF (i % 2 == 0) set result += 2 * arr_2[i] End Else set result += 4 * arr_2[i] End set result *= (step_x / 3) End return result Step 2-> In main() declare step for x as float step_x = 1.2 Declare step for y as float step_y = 0.54 Declare lower limit of xfloat lower_x = 1.3 Declare upper limit of xfloat upper_x = 2.1 Declare lower limit of yfloat lower_y = 1.0 Declare upper limit of yfloat upper_y = 2.1 Call (step_x, step_y, lower_x, upper_x, lower_y, upper_y) Stop
示例
#include <bits/stdc++.h>
using namespace std;
float fun(float x, float y) {
return pow(pow(x, 4) + pow(y, 5), 0.5);
}
// Function to find the double integral value
float doubleIntegral(float step_x, float step_y, float lower_x, float upper_x, float lower_y, float upper_y) {
int n1, n2;
float arr[50][50], arr_2[50], result;
n1 = (upper_x - lower_x) / step_x + 1;
n2 = (upper_y - lower_y) / step_y + 1;
for (int i = 0; i < n1; ++i) {
for (int j = 0; j < n2; ++j) {
arr[i][j] = fun(lower_x + i * step_x, lower_y + j * step_y);
}
}
for (int i = 0; i < n1; ++i) {
arr_2[i] = 0;
for (int j = 0; j < n2; ++j) {
if (j == 0 || j == n2 - 1)
arr_2[i] += arr[i][j];
else if (j % 2 == 0)
arr_2[i] += 2 * arr[i][j];
else
arr_2[i] += 4 * arr[i][j];
}
arr_2[i] *= (step_y / 3);
}
result = 0;
for (int i = 0; i < n1; ++i) {
if (i == 0 || i == n1 - 1)
result += arr_2[i];
else if (i % 2 == 0)
result += 2 * arr_2[i];
else
result += 4 * arr_2[i];
}
result *= (step_x / 3);
return result;
}
int main() {
float step_x = 1.2; //steps for x
float step_y = 0.54; //steps for y
float lower_x = 1.3; //lower limit of x
float upper_x = 2.1; //upper limit of x
float lower_y = 1.0; //lower limit of y
float upper_y = 2.1; //upper limit of y
cout<<"double integration is : "<<(step_x, step_y, lower_x, upper_x, lower_y, upper_y);
return 0;
}輸出
double integration is : 2.1
更新日期：20-11-2019
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