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
A reliable approach for analysing the nonlinear KdV equation of fractional order
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
‎Korteweg-de Vries fractional time equation‎, ‎Crank-Nicolson difference method‎, ‎Caputo fractional derivative
سال
2022
مجله Journal of Applied Analysis and Computation
پژوهشگران خسرو سایوند

چکیده

‎Its applications in many domains‎, ‎along with its challenging analytical solution‎, ‎have led to several studies of the Korteweg-de Vries (KdV) equation over the past decade‎. ‎Due to difficulties or impossibility with the analytical solution to this equation‎, ‎the paper presents a numerical solution using the Crank-Nicolson difference method‎. ‎A study of the stability and solvency of this method has been undertaken‎. ‎In this paper‎, ‎we prove that the scheme is first order convergent in space and $\min \{ 2‎ - ‎\nu‎ ,‎r\nu \} $ order convergent in time‎, ‎where $ r$ refers to a gradation parameter and $\nu$ represents the fractional derivative‎. ‎The results are then presented in numerical applications‎, ‎looking at how it compares with other sophisticated schemes in the literature‎. ‎The main benefit of the proposed scheme is the efficiency with regard to accuracy as compared to other available schemes‎.