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72 lines
2.4 KiB
C++
72 lines
2.4 KiB
C++
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/*------- MODIFIED EULER'S METHOD TO SOLVE DIFFERENTIAL EQUATION ------*/
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/* THIS PROGRAM CALCULATES THE VALUE y AT GIVEN VALUE OF x
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USING MODIFIED EULER'S METHOD. THE FUNCTION y' = f(x,y) IS
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DEFINED IN THE PROGRAM.
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y' = x*x + y
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Hence f(x,y) = x*x + y
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INPUTS : 1) Initial values of x and y.
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2) Step size h.
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OUTPUTS : Calculated values of y at every step. */
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/*------------------------------ PROGRAM --------------------------*/
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#include<stdio.h>
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#include<math.h>
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#include<stdlib.h>
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#include<conio.h>
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void main()
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{
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double f (double x0,double y0); /* DECLARATION OF A FUNCTION f */
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double y0,y1,y10,x0,x1,h,x,diff;
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int i,n;
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clrscr();
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printf("\n\tMODIFIED EULER'S METHOD TO SOLVE DIFFERENTIAL EQUATION");
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printf("\n\nEnter x0 = ");
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scanf("%lf",&x0); /* ENTER VALUE OF x0 */
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printf("\n\nEnter y0 = ");
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scanf("%lf",&y0); /* ENTER VALUE OF y0 */
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printf("\n\nEnter the value of x at which y is to be found = ");
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scanf("%lf",&x); /* ENTER VALUE OF x */
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printf("\n\nEnter the value of h = ");
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scanf("%lf",&h); /* ENTER THE VALUE OF h */
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i = 0;
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printf("\nPress any key to see step by step display of results...\n");
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while(x0 < x) /* LOOP TO CALCULATE y USING MODIFIED EULER'S FORMULA*/
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{
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i++;
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x1 = x0 + h;
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y1 = y0 + h * f(x0,y0); /* PREDICTOR EQUATION */
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y10 = y1;
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do /* LOOP TO IMPLEMENT CORRECTOR FORMULA */
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{
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y1 = y0 + (h/2) * ( f(x0,y0) + f(x1,y10) );
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diff = fabs(y1 - y10); /* CHECK FOR HOW MANY DIGITS
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ARE REPEATING AFTER DECIMAL POINT*/
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y10 = y1;
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}
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while( diff > 0.0001);
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/*REMAIN IN LOOP TILL 3 DIGITS REPEAT AFTER DECIMAL POINT*/
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printf("\nx%d = %lf y%d = %lf",i,x1,i,y1);
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x0 = x1;
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y0 = y1;
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getch();
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}
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}
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/*---------------------------------------------------------------------*/
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double f ( double x,double y) /* FUNCTION TO CALCULATE VALUE OF f(x,y)*/
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{
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double y_dash;
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y_dash = x*x + y; /* function f(x,y) = y' = x*x + y */
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return(y_dash);
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}
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/*------------------------ END OF PROGRAM -----------------------------*/
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