. , , ,

,,,

—

.

" "

"Research of Accuracy of Numerical Integration"

"",

: ..

: .

..

: -207

2000

1.   .................................................................. 3

2.   ................... 3

3.   ............................................................. 4

4.   .............................................................. 12

5.   ................................... 13

6.   ........................................................................ 13

, .

, . , [a,b] n ().

n. .

.

.

, , .

( )

,

,

-0,1676631 14
-0,1518916 16
-0,0046931 12
-0,0026531 11
-0,0002639 10
-0,0001709 2
-0,0001297 9
-0,0000557 3
-0,000025 8
-0,0000198 4
-0,0000096 5
-0,0000038 6
0 15
0,0000052 7
0,071089 13


-0,1127271 16
-0,0750288 15
-0,0540677 14
-0,0021415 12
-0,0005711 11
-0,0000458 9
-0,0000381 2
-0,0000191 3
-0,000008 4
-0,000004 5
-0,0000019 7
-0,0000002 6
0,000005 8
0,0002983 10
0,0164377 13


-0,0066709 13
-0,0042367 14
-0,0003561 10
-0,0000016 5
-0,000001 4
0,0000005 3
0,0000006 6
0,0000009 2
0,0000009 7
0,0000223 8
0,000056 9
0,0002782 11
0,0003474 12
0,005293 16
0,0053267 15


-61,4469795 12
-5,714047 3
-1,0215755 13
-0,7241433 2
-0,5121117 4
-0,3222643 11
-0,2163614 7
-0,1536629 9
-0,0930261 14
0,0353183 16
0,057059 15
0,1697371 5
0,2025534 10
0,2504728 6
0,6202592 8


-0,0119308 16
-0,0007834 13
-0,0000079 3
-0,0000041 4
-0,0000037 7
-0,0000027 5
-0,0000027 6
-0,000002 8
-0,0000016 2
0,0000003 10
0,0000062 9
0,0000385 11
0,0000802 12
0,0005452 15
0,0016689 14


-0,0026286 16
-0,0012416 14
-0,0000118 3
-0,0000107 4
-0,0000046 5
-0,0000046 9
-0,0000028 6
-0,0000021 7
-0,0000005 2
0,0000011 10
0,0000018 8
0,0000023 11
0,000058 12
0,0001049 13
0,0027928 15


-0,0001709 2 -0,0001932 2
-0,0000557 3 -0,0000629 3
-0,0000198 4 -0,0000224 4
-0,0000096 5 -0,0000108 5
-0,0000038 6 -0,0000043 6
0,0000052 7 0,0000058 7
-0,000025 8 -0,0000283 8
-0,0001297 9 -0,0001466 9
-0,0002639 10 -0,0002983 10
-0,0026531 11 -0,002998 11
-0,0046931 12 -0,0052891 12
0,071089 13 0,0797403 13
-0,1676631 14 -0,2014365 14
0 15 0 15
-0,1518916 16 -0,1518916 16


 

 
-0,0000381 2 -0,0000666 2

 
-0,0000191 3 -0,0000335 3

 
-0,000008 4 -0,0000141 4

 
-0,000004 5 -0,0000069 5

 
-0,0000002 6 -0,0000004 6

 
-0,0000019 7 -0,0000033 7

 
0,000005 8 0,0000088 8

 
-0,0000458 9 -0,0000802 9

 
0,0002983 10 0,000522 10

 
-0,0005711 11 -0,0009997 11

 
-0,0021415 12 -0,0037465 12

 
0,0164377 13 0,0286955 13

 
-0,0540677 14 -0,0959378 14

 
-0,0750288 15 -0,1259331 15

 
-0,1127271 16 -0,1750124 16

 



 




n=1000000

n =1000000
4,5051475 4,5240183 4,49980967 f(x)=1/x 0,1..9
1,7491462 1,7500761 1,791756469 f(x)=1/x*x 0,3..5
1,9991885 1,9999505 2 f(x)=sin(x) 0.π
-0,0000512 0,000003 0 f(x)=sin(2*x) 0.π
0,2857157 0,2856935 0,285714285 f(x)=sin(7*x) 0....π
0,2222053 0,2222133 0,222222222 f(x)=sin(9*x) 0....π

4,49980967 4,5217996 9 -0,02198993
4,605170186 4,624969 10 -0,019798814
4,787491743 4,8039412 12 -0,016449457
4,941642423 4,9557843 14 -0,014141877
5,075173815 5,0875444 16 -0,012370585
5,192956851 5,2039275 18 -0,010970649
5,298317367 5,3082042 20 -0,009886833

,

1.    / .., ..-.:- , 1998.

/*

" "

"Research of Accuracy of Numerical Integration"

:

: ..

..

: -207

*/

# include <stdio.h>

# include <io.h>

# include <stdlib.h>

# include <iostream.h>

# include <string.h>

# include <math.h>

int main ()

{

FILE *fp; /* */

int n,i,t,j,N;

float a,b,h,Sum[100],x,y,coa;

printf("Research of Accuracy of Numerical Integration\n");

/* */

printf("Enter accuracy of calculation n= ");

scanf("%d",&n);

/* */

printf("Enter beginnings of integration= ");

scanf("%f",&a);

/* */

printf("Enter limit of integration= ");

scanf("%f",&b);

 

/* -*/

while((fp=fopen("data3.xls","w"))==NULL)

{

puts("Error!!! Can't open file \nInput name of file\n");

}

/* */

printf("Enter number of Itteration N= ");

scanf("%d",&N);

/* */

h=(a+b)/n;

printf("Step=%.3f\n",h);

/******* *******/

for(j=1;j<=N;j++)

{

h=(a+b)/(int(pow(2,j-1))*n);

Sum[j]=0;

for(i=0;i<=(int(pow(2,j-1))*n);i++)

{

x=a+i*h;

if(i==0)

t=1;

else

t=2;

y=t*(h/2)*(sin(2*x));

Sum[j]=Sum[j]+y;

}

if (j>1)

{

coa=(Sum[j]-Sum[j-1])/Sum[j-1];

printf("Criterion of accuracy=%.5f Number of iteration=%d\n",coa,j);

fprintf(fp,"%.7f\t",coa);

fprintf(fp,"%d\t\n",j);

}

}

printf("The sum by a method of trapezes=%.7f\n",Sum[1]);

fprintf(fp,"The sum by a method of trapezes=%.7f\n",Sum[1]);

/******* *******/

for(j=1;j<=N;j++)

{

h=(a+b)/(int(pow(2,j-1))*n);

Sum[j]=0;

for(i=0;i<=(int(pow(2,j-1))*n);i++)

{

x=a+i*h;

if(i==0||i==n)

t=1;

else

{

if(i%2==0)

t=2;

else

t=4;

}

y=t*(h/3)*(sin(2*x));

Sum[j]=Sum[j]+y;

}

if (j>1)

{

coa=(Sum[j]-Sum[j-1])/Sum[j-1];

printf("Criterion of accuracy=%.5f Number of iteration=%d\n",coa,j);

fprintf(fp,"%.7f\t",coa);

fprintf(fp,"%d\t\n",j);

}

}

printf("The sum by a Simpson's method= %.7f\n",Sum[1]);

fprintf(fp,"The sum by a Simpson's method=%.7f\n",Sum[1]);

scanf("%d",&b);

}

. &quot; &quot; &qu

 

 

 

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