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An accurate finite-difference scheme for the numerical solution of a fractional differential equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 مهر 1403 اصل مقاله (1.33 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.61919.2699 | ||
| نویسندگان | ||
| Aniruddha Seal؛ Srinivasan Natesan* | ||
| Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781039, India. | ||
| چکیده | ||
| In this article, a steady-state fractional order boundary-value problem is considered with a fractional convection term. The highest-order derivative term involves a mixed-fractional derivative which appears as a combination of a first-order classical derivative and Caputo fractional derivative. We propose an $L1-$scheme over a uniform mesh for the numerical solution of the fractional differential equation. With the help of a properly chosen barrier function, we discuss error analysis and prove that the proposed method converges with almost first-order. The proposed scheme is also applied on a semilinear fractional differential equation. Numerical experiments are presented to validate the proposed method. | ||
| کلیدواژه‌ها | ||
| Fractional Differential Equation؛ $L1-$method؛ Discrete Comparison Principle؛ Stability؛ Convergence | ||
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آمار تعداد مشاهده مقاله: 262 تعداد دریافت فایل اصل مقاله: 274 |
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