(594) Fortran Subroutine For Simpson's Method of Numerical Integration روتين فرعي بلغة فورتران لطريقة سيمبسون للتكامل العددي - A. Sedrac, Khairy; Hamid, S. (INP, 2024)
The study discusses Simpson's method for numerical integration using a Fortran subroutine. The routine aims to compute the numerical integral of the function \( f(x) \) from point \( a \) to point \( b \) using Simpson's one-third rule. The function is evaluated at \( n+1 \) points, dividing the interval into smaller segments. Simpson's rule states that the integral can be computed using a combination of function values at various points. The routine starts with an initial interval \( n \) and repeats the computation by doubling the interval to achieve a more accurate estimate of the integral. The truncation error is compared with a user-defined tolerance, and if the error exceeds this value, the process is repeated by doubling the intervals for improved results.