01 تیر 1403
خسرو سايوند

خسرو سایوند

مرتبه علمی: استاد
نشانی: ملایر گروه ریاضی دانشگاه ملایر
تحصیلات: دکترای تخصصی / ریاضی
تلفن: 081-33398981
دانشکده: دانشکده علوم ریاضی و آمار

مشخصات پژوهش

عنوان
On fractional Kakutani–Matsuuchi water wave model: Implementing a reliable implicit finite difference method
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
backward Euler differences, finite difference method, fractional water wave equation, Riemann–Liouville fractional derivatives, trapezoidal quadrature rule
سال
2021
مجله Mathematical Methods in the Applied Sciences
پژوهشگران خسرو سایوند

چکیده

In this study, a reliable implicit finite difference method based on the modified trapezoidal quadrature rule, backward Euler differences, nonstandard central approximations, and the Hadamard finite-part integral is being considered to solve a viscous asymptotical model named as fractional Kakutani–Matsuuchi water wave model. The fractional derivative is used in the Riemann–Liouville sense. Based on the properties of Brouwer's fixed-point theorem, the existence, uniqueness, convergence, and stability of the proposed method are proved. Furthermore, we show that the global convergence order of the method in maximum norm is O ( 휏 , h min { 훽 ,3 − 훼 } ), where 0 <훼 ≤ 1and 훽> 0 are the order of fractional derivative and the Lipschitz constant. Also, 휏 and h are the time step and space step, respectively. Finally, several examples are used to illustrate the accuracy and performance of the method.