scholarly journals Application of Laplace residual power series method for approximate solutions of fractional IVP’s

2021 ◽  
Author(s):  
Mohammad Alaroud
Keyword(s):  
Power Series ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power

scholarly journals Approximate Solutions of Two-Dimensional Burgers' and Coupled Burgers' Equations by Residual Power Series Method

2018 ◽  
Vol 22 ◽  
pp. 01044
Author(s):  
Selahattin Gulsen ◽  
Mustafa Inc ◽  
Harivan R. Nabi
Keyword(s):  
Power Series ◽  
Taylor Series Expansion ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Series Method ◽  
Power Series Method ◽  
Burgers Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power

In this study, two-dimensional Burgers' and coupled Burgers' equations are examined by the residual power series method. This method provides series solutions which are rapidly convergent and their components are easily calculable by Mathematica. When the solution is polynomial, the method gives the exact solution using Taylor series expansion. The results display that the method is more efficient, applicable and accuracy and the graphical consequences clearly present the reliability of the method.

scholarly journals Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 799-805
Author(s):  
Gamal Mohamed Ismail ◽  
Hamdy Ragab Abdl-Rahim ◽  
Hijaz Ahmad ◽  
Yu-Ming Chu
Keyword(s):  
Power Series ◽  
Fractional Derivatives ◽  
Approximate Solutions ◽  
Series Method ◽  
Fractional Partial Differential Equation ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Physical Phenomena ◽  
Residual Power

AbstractIn this article, analytical exact and approximate solutions for fractional physical equations are obtained successfully via efficient analytical method called fractional residual power series method (FRPSM). The fractional derivatives are described in the Caputo sense. Three applications are discussed, showing the validity, accuracy and efficiency of the present method. The solution via FRPSM shows excellent agreement in comparison with the solutions obtained from other established methods. Also, the FRPSM can be used to solve other nonlinear fractional partial differential equation problems. The final results are presented in graphs and tables, which show the effectiveness, quality and strength of the presented method.

scholarly journals Approximate solutions and conservation laws of the periodic base temperature of convective longitudinal fins in thermal conductivity

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 267-273
Author(s):  
Isa Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Thermal Conductivity ◽  
Power Series ◽  
Linear Models ◽  
Approximate Solutions ◽  
Base Temperature ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power

In this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.

scholarly journals Residual power series method for solving nonlinear reaction-diffusion-convection problems

2021 ◽  
Vol 39 (3) ◽  
pp. 177-188
Author(s):  
Maisa Khader ◽  
Mahmoud H. DarAssi
Keyword(s):  
Power Series ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Nonlinear Reaction ◽  
Residual Power Series ◽  
Diffusion Convection ◽  
Residual Power

In this paper, the residual power series method (RPSM) is applied to one of the most frequently used models in engineering and science, a nonlinear reaction diffusion convection initial value problems. The approximate solutions using the RPSM were compared to the exact solutions and to the approximate solutions using the homotopy analysis method.

scholarly journals Residual Power Series Method for Solving Klein-Gordon Schrödinger Equation

2021 ◽  
Vol 9 (2) ◽  
pp. 123-127
Author(s):  
Ssaad A. Manaa ◽  
Fadhil H. Easif ◽  
Jomaa J. Murad
Keyword(s):  
Power Series ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Klein Gordon ◽  
Residual Power

In this work, the   Residual Power Series Method(RPSM) is used to find the approximate solutions of Klein Gordon Schrödinger (KGS) Equation. Furthermore, to show the accuracy and the efficiency of the presented method, we compare the obtained approximate solution of Klein Gordon Schrödinger equation by Residual Power Series Method(RPSM) numerically and graphically with the exact solution.

scholarly journals Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Anas Arafa ◽  
Ghada Elmahdy
Keyword(s):  
Power Series ◽  
Power Efficiency ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Homotopy Analysis ◽  
Residual Power Series ◽  
Residual Power

The approximate analytical solution of the fractional Cahn-Hilliard and Gardner equations has been acquired successfully via residual power series method (RPSM). The approximate solutions obtained by RPSM are compared with the exact solutions as well as the solutions obtained by homotopy perturbation method (HPM) and q-homotopy analysis method (q-HAM). Numerical results are known through different graphs and tables. The fractional derivatives are described in the Caputo sense. The results light the power, efficiency, simplicity, and reliability of the proposed method.

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