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Solution of non-homogeneous dynamic equation on time scale | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 اردیبهشت 1404 اصل مقاله (1.19 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65428.3009 | ||
| نویسندگان | ||
| Ahmed Azaba1؛ Kamal R. Raslan2؛ Khalid K. Ali* 2 | ||
| 1Al-Ryada University for Science and Technology, Sadat City, Menoufia, Egypt. | ||
| 2Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt. | ||
| چکیده | ||
| We find the general solution to the non-homogeneous dynamic equation, which is a combination of discrete and continuous mathematics. The nature of this equation requires a careful approach, as it involves elements of both types of math, making it both versatile and challenging. To address this, we will derive the formula for the general solution of the non-homogeneous equation, incorporating given initial conditions. During this process, we will define several critical points that may be either discrete, continuous, or a mix of both. By analyzing these points, we aim to capture the essence of the dynamic behavior of the system. Our approach involves finding an analytical solution to the equation and comparing it with a numerical approximation to evaluate their accuracy. We will graph both the analytical and numerical solutions to visualize their behavior and identify any discrepancies. Additionally, we will calculate the absolute error between the exact solution and the numerical solution to quantify the differences precisely. This comparison provides valuable insights into the accuracy and stability of numerical methods for solving such equations. Finally, we will demonstrate this approach by applying it to various examples, showcasing the methodology's effectiveness in solving a range of non-homogeneous dynamic equations with different initial conditions and parameters. | ||
| کلیدواژه‌ها | ||
| Time Scale؛ Non-Homogenous dynamic equation؛ Numerical solution؛ Initial Value Problem؛ General Solution | ||
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آمار تعداد مشاهده مقاله: 45 تعداد دریافت فایل اصل مقاله: 46 |
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