Wednesday - June 5, 2024
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Fortran ~ Trapezoidal rule

Fortran Trapezoidal rule

  • Some trapezium rule is a method of estimating the area under a curve.
  • We have known that the area under a curve is given by integration, so the trapezium rule gives a method of estimating integrals.
  • That is useful if we come across integrals that we don’t call whence to evaluate.
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Q.  Write a Program using the Trapezoidal rule to Calculate the area under a curve…?

PROGRAM TRULY


C
C         PROGRAM TO DEMONSTRATE THE APPLICATION OF THE TRAPEZOIDAL RULE
C
C        THIS PROGRAM NUMERICALLY INTEGRATES GIVEN EXPRESSION WITHIN
C        SPECIFIED LIMITS OF INTEGRATION
C        AS INTEGRAL OF A FUNCTION IS EQUAL TO THE AREA UNDER THE CURVE
C        WE CAN ALSO USE THE PROGRAM TO CALCULATE THE AREA UNDER A CURVE
C
           F(X)=3.12*X**3+1.54*X**2-6.23
C
          WRITE(*,*)'LIMITS OF INTEGRATION(A,B)'
          READ(*,*)A,B
          WRITE(*,*)'NUMBER OF STRIPES'
          READ(*,*)NS
C       STRIP SIZE
          H=(B-A)/NS
          AREA=F(A)+F(B)
          DO 100 X=A+H,B-H,H
          AREA=AREA+2.0*F(X)
100    CONTINUE
          AREA=AREA*H/2.0
          WRITE(*,*)'AREA UNDER THE CURVE=',AREA
          STOP
          END


#OUTPUT
LIMIT OF INTEGRATION (A, B)
0 6
NUMBER OF STRIPS
6
AREA UNDER THE CURVE = 159.00000