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 Computational Efficiency and Dynamical Analysis for a Class of Novel Multi-step Iterative Schemes
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
Iterative schemes · Multi-step scheme · Computational efficiency · Systems of nonlinear equations · Fractional calculus
سال
2021
مجله International Journal of Applied and Computational Mathematics
پژوهشگران خسرو سایوند

چکیده

This paper presents a novel multi-step iterative scheme to solve system of nonlinear equa- tions. Because the cost of calculating the Fréchet derivative evaluation and its inversion is significant, in order to achieve its high computational efficiency, we have tried to calculate Fréchet derivative and its inverse less per cycle by using the proposed multi-step iterative schemes. The basic iterative scheme has a convergence order of four; therefore, repetition of the second step can achieve higher convergence order. In fact, adding a new step to the base iterative scheme each time increases the convergence order by two units. The multi-step iterative schemes have convergence-order 2 m ,where m is the number of steps of the multi- step iterative schemes. Also, the computational efficiency of the iterative scheme is compared with other available methods. The numerical results presented confirm the theoretical results. A number of nonlinear system of equations associated with the numerical approximation of ordinary, partial, and fractional differential equations are made up and solved.