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Exploring Mathematical Modeling of Non-linear Inviscid and Viscid Burgers’ Equations: A Comprehensive Study | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 خرداد 1405 اصل مقاله (1.18 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.67577.3227 | ||
| نویسنده | ||
| Pragneshkumar R. Makwana* | ||
| Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa-388421, Gujarat, India. | ||
| چکیده | ||
| Present study investigates the application of the power series method to solve non-linear inviscid and viscid Burgers’ equations, a fundamental equation for modeling various physical phenomena that include fluid dynamics and traffic flow. We derive approximate solutions under specific initial conditions, demonstrating the effectiveness of the power series approach for obtaining accurate results. The solutions obtained are expressed in series form, which can be further simplified into closed analytic forms. Our findings indicates that the accuracy of the derived solutions improves with the inclusion of additional terms in the series expansion. This research highlights the advantages of the power series method in solving a robust mathematical tool for addressing dynamical systems with non-linearity. It provides solution with accuracy, efficiency, and minimal computations. | ||
| کلیدواژهها | ||
| Power Series Method؛ Non-linear Burgers’ Equation؛ Mathematical Modeling | ||
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آمار تعداد مشاهده مقاله: 5 تعداد دریافت فایل اصل مقاله: 7 |
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