Improving Homotopy Analysis Method with An Optimal Parameter for Time-Fractional Burgers Equation
نویسندگان
چکیده
The aim of the study is to reduce absolute error by determining optimal value this arbitrary parameter using residual function related selection h. Some numerical examples are solved and compared existing results. homotopy analysis method has been successfully implemented Burgers equation obtain serial solutions. On base solutions obtained for required equations, it shown that applicable time-fractional partial differential equations.
منابع مشابه
Approximate Analytical Solution of Diffusion Equation with Fractional Time Derivative Using Optimal Homotopy Analysis Method
In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution...
متن کاملHomotopy perturbation method for solving fractional Bratu-type equation
In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...
متن کاملAn Efficient Method for Systems of Variable Coefficient Coupled Burgers' Equation with Time-Fractional Derivative
A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...
متن کاملHomotopy Analysis Method for Solving Fractional Diffusion Equation
In this letter, the powerful, easy-to-use and effective mathematical tool like Homotopy Analysis Method is used to solve the diffusion equation with fractional time derivative ) 1 0 ( . Using the initial condition, the approximate analytical solution of the problem is obtained. Choosing proper values of auxiliary and homotopy parameters, the convergence of the approximate series solution...
متن کاملSymmetry analysis of time-fractional potential Burgers' equation
Lie point symmetries of time-fractional potential Burgers' equation are presented. Using these symmetries fractional potential Burgers' equation has been transformed into an ordinary differential equation of fractional order corresponding to the Erdélyi-Kober fractional derivative. Further, an analytic solution is furnished by means of the invariant subspace method. AMS subject classifications:...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Karamano?lu Mehmetbey Üniversitesi Mühendislik ve Do?a Bilimleri dergisi
سال: 2022
ISSN: ['2687-5071']
DOI: https://doi.org/10.55213/kmujens.1206517