Re: [問題]使用辛普森法做積分
※ 引述《nat000 (天濤˙流)》之銘言：
: 我想用辛普森法做出積分且增加一容差參數。
: 計算N=2與N=4之結果的差值，若差值比容差大，則增加N值。
: 重複第二步，直至差值小於容差時，輸出積分結果與此時差值。
: 寫到檢驗n=4和n=2的差時就卡關了
: 我不知道要如何表示result(n=4)-result(n=2)這一句
: 我用的編譯器是Dev-C++
: 以下是我的程式碼
: #include <stdio.h>
: int main(void)
: {
: double a0, a1, a2, a3;
// coefficients, g'(x) = a3*x^3 + a2*x^2+ a1*x + a0
: double a, b; // integration interval, [a, b]
: int N; // number of segments, N
: double h; // length of each segments, dx
: double x0, x1, x2
// 3 sample points for simpson's method, x
: double f0, f1, f2; // value at 3 sample points, f(x)
: int counter; // number of segment count
: double result = 0; // result of integral
: //get coefficient and interval from user
: printf("**** Integration by simpson's method **** \n"
: "Integral g'(x) dx at interval [a,b]\n\n");
: printf("Please input coeficients for g'(x) = a3*x^3 + a2*x^2 + a1*x + a0
: \n>");
: scanf("%lf%lf%lf%lf", &a3, &a2, &a1, &a0\n");
printf("Please input parameter interval [a,b] \n>");
: scanf("%lf%lf", &a, &b);
: //get number of segment
: printf("Please input the number of segments \n>");
: scanf("%d", &N);
: while( N > 0 )
: {
: //clear result for each loop
: result = 0;
: //check N
: if( N % 2 != 0)
: {
: printf("N must be a even number!
\nProgram if force to end.\n");
: return 0;
: }
: //calculate length of segment
: h = (b - a) / N;
: //initialize x to first segment
: x0 = a;
: x1 = a + h;
: x2 = a + 2*h;
: //calculation by simpson's method for each segment
: for( counter = 1 ; counter <= N/2 ; counter++ )
: {
: //calculate value at 3 sample points
: f0 = a3*x0*x0*x0 + a2*x0*x0 + a1*x0 + a0;
: f1 = a3*x1*x1*x1 + a2*x1*x1 + a1*x1 + a0;
: f2 = a3*x2*x2*x2 + a2*x2*x2 + a1*x2 + a0;
: //add to result by simpson's rule
: result = result + h/3 * (f0 + 4.0*f1 + f2);
: //move the 3 sample point to next segment
: x0 = x0 + 2*h;
: x1 = x1 + 2*h;
: x2 = x2 + 2*h;
: }//end for
: //print out result
: printf("The result of the integration is %lf\n", result);
: //check for re-loop
: printf("\nDo you want to rechoose the number of segments?
(enter -1 to leave)\n>");
: scanf("%d", &N );
: }//end while
: return 0;
--
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