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Write a program (fortran 90) that calls a subroutine to approximate the derivative of y=sin(x)+2x^2 using...

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Advance Math

Write a program (fortran 90) that calls a subroutine toapproximate the derivative of y=sin(x)+2x^2 using a one-sideddifference approach fx = (fi-fi-1)/deltaX and a centered differenceapproach fx = (fi+1-fi-1)/deltaX. The value of the function f andits derivative fx should be evaluated at x=3.75. Your code shouldprint both values tot he screen when it runs.

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3.6 Ratings (628 Votes)

! Fortran Programe

PROGRAM Approx_Der
IMPLICIT NONE
REAL :: x,deltaX, y, One_side_Diff, Central_Diff   
x=3.75
deltaX = 0.1
One_side_Diff = (y(x)-y(x-deltaX))/deltaX
Central_Diff = (y(x+deltaX)-y(x-deltaX))/deltaX
PRINT *, 'approximated derivative of y at point x = 3.75 using One Sided Difference : ', One_side_Diff
PRINT *, 'approximated derivative of y at point x = 3.75 using Central Difference: ', Central_Diff
END PROGRAM Approx_Der

FUNCTION y(x)
IMPLICIT NONE
REAL :: y   
REAL, INTENT( IN ) :: x
y =SIN(x)+2*x**2
  
END FUNCTION y

! output

approximated derivative of y at point x = 3.75 using One Sided Difference :     13.9522362                                   

approximated derivative of y at point x = 3.75 using Central Difference:     28.3615875
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