Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method

سال انتشار: 1404
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 141

فایل این مقاله در 15 صفحه با فرمت PDF قابل دریافت می باشد

استخراج به نرم افزارهای پژوهشی:

لینک ثابت به این مقاله:

شناسه ملی سند علمی:

JR_CMDE-13-2_009

تاریخ نمایه سازی: 27 فروردین 1404

چکیده مقاله:

This paper presents a numerical scheme for solving the non-linear time fractional Klein-Gordon equation. To approximate spatial derivatives, we employ the pseudo-spectral method based on Lagrange polynomials at Chebyshev points, while using the finite difference method for time discretization. Our analysis demonstrates that this scheme is unconditionally stable, with a time convergence order of \mathcal{O}({۳ \alpha}). Additionally, we provide numerical results in one, two, and three dimensions, highlighting the high accuracy of our approach. The significance of our proposed method lies in its ability to efficiently and accurately address the non-linear time fractional Klein-Gordon equation. Furthermore, our numerical outcomes validate the effectiveness of this scheme across different dimensions.

نویسندگان

Soheila Mirzaei

Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan, Iran.

Ali Shokri

Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan, Iran.