Fortran Subroutine For Simpson's Method of Numerical Integration
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, dividi...
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2024
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| _version_ | 1853147126077325312 |
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| author | A. Sedrac, Khairy Hamid, S. |
| author_facet | A. Sedrac, Khairy Hamid, S. |
| author_sort | A. Sedrac, Khairy |
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| description | 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. |
| format | Book |
| id | oai:repository.inp.ed.eg:123456789-5840 |
| institution | My University |
| publishDate | 2024 |
| publisher | INP |
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| spelling | oai:repository.inp.ed.eg:123456789-58402025-02-13T11:46:46Z Fortran Subroutine For Simpson's Method of Numerical Integration A. Sedrac, Khairy Hamid, S. Fortran Simpson's Method Numerical Integration 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. يتناول البحث طريقة سيمبسون للتكامل العددي باستخدام روتين فرتران. يهدف الروتين إلى حساب التكامل العددي للدالة \( f(x) \) من النقطة \( a \) إلى النقطة \( b \) باستخدام قاعدة سيمبسون للثلث. يتم حساب الدالة عند \( n+1 \) نقطة، حيث يتم تقسيم الفترة إلى فترات صغيرة. تنص قاعدة سيمبسون على أن التكامل يمكن حسابه من خلال تركيبة من قيم الدالة عند النقاط المختلفة. يبدأ الروتين بتحديد الفترة الأولية \( n \) ثم يقوم بتكرار الحساب عن طريق مضاعفة الفترة للحصول على تقدير أكثر دقة للتكامل. يتم مقارنة خطأ التقريب بالقيمة المعطاة من قبل المستخدم، وإذا تجاوز الخطأ هذه القيمة، يتم تكرار العملية مع مضاعفة الفترة للحصول على نتائج أفضل. 2024-12-29T13:38:09Z 2024-12-29T13:38:09Z 1965-05 Book http://repository.inp.edu.eg//handle/123456789/5840 سلسلة مذكرات خارجية رقم (594); application/pdf INP |
| spellingShingle | Fortran Simpson's Method Numerical Integration A. Sedrac, Khairy Hamid, S. Fortran Subroutine For Simpson's Method of Numerical Integration |
| title | Fortran Subroutine For Simpson's Method of Numerical Integration |
| title_full | Fortran Subroutine For Simpson's Method of Numerical Integration |
| title_fullStr | Fortran Subroutine For Simpson's Method of Numerical Integration |
| title_full_unstemmed | Fortran Subroutine For Simpson's Method of Numerical Integration |
| title_short | Fortran Subroutine For Simpson's Method of Numerical Integration |
| title_sort | fortran subroutine for simpson s method of numerical integration |
| topic | Fortran Simpson's Method Numerical Integration |
| url | http://repository.inp.edu.eg//handle/123456789/5840 |
| work_keys_str_mv | AT asedrackhairy fortransubroutineforsimpsonsmethodofnumericalintegration AT hamids fortransubroutineforsimpsonsmethodofnumericalintegration |