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Application of Variational Calculus to Integrability of Differential Equations with Physical Applications | ||
| International Journal of Industrial Mathematics | ||
| دوره 15، شماره 2، مهر 2023، صفحه 165-174 اصل مقاله (456.47 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.30495/ijim.2023.72830.1665 | ||
| نویسنده | ||
M. Pakdemirli  
| ||
| Mechanical Engineering Department, Manisa Celal Bayar University, Muradiye, Yunusemre, Manisa, Turkey. | ||
| چکیده | ||
| Variational calculus is used to determine the integrability of differential equations. A remarkable unified approach is presented by a single theorem employing variational calculus to determine the integrability of any ordinary differential equation whether linear or nonlinear. The theorem is also used to determine the integrating factor for a given equation if it is not directly integrable. Well established results for determining integrating factors obtained by various methods can be combined in a single equation of variational calculus. Many sample problems are extensively treated to show the power and applicability of the theorem. The method is applied to a variety of problems stemming from physical phenomena. | ||
| کلیدواژهها | ||
| Variational Calculus؛ Integrability؛ Differential Equations؛ Integrating Factor؛ Mathematical Physics Applications | ||
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آمار تعداد مشاهده مقاله: 12 تعداد دریافت فایل اصل مقاله: 23 |
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