Applications of General Residual Power Series Method to Differential Equations with Variable Coefficients [PDF]
Discrete Dynamics in Nature and Society, 2018 This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations ...
Bochao Chen, Li Qin, Fei Xu, Jian Zu
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An Improved Version of Residual Power Series Method for Space-Time Fractional Problems [PDF]
Advances in Mathematical Physics, 2022 The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter
Mine Aylin Bayrak +2 more
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Fractal and Fractional, 2023 In this paper, we present an efficient solution method for solving fractional system partial differential equations (FSPDEs) using the Laplace residual power series (LRPS) method.
Ahmad Shafee +2 more
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Dynamical analysis of a nonlinear oscillator chain in the Peyrard–Bishop DNA model using residual power series and Laplace residual power series method [PDF]
Iranian Journal of Numerical Analysis and OptimizationIn this study, we investigate the numerical exploration of the Peyrard–Bishop DNA (PBD) dynamic model. These solutions are responsible for analyzing the nonlinear interactions between the adjacent displacements of the DNA strand.
D. Priyadarsini, P.K. Sahu, M. Routaray
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A Numerical Solution of Fractional Lienard’s Equation by Using the Residual Power Series Method [PDF]
Mathematics, 2017 In this paper, we investigate a numerical solution of Lienard’s equation. The residual power series (RPS) method is implemented to find an approximate solution to this problem.
Muhammed I. Syam
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Analytical treatment of the fractional Zakharov–Kuznetsov equation via the generalized integral residual power series method [PDF]
Scientific ReportsThis study presents a generalized integral residual power series method (GIRPSM) for finding semi-analytical solutions to the nonlinear fractional Zakharov–Kuznetsov equation (FZKE).
Samy A. Abdelhafeez +4 more
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Laplace-Residual Power Series Method for Solving Time-Fractional Reaction–Diffusion Model
Fractal and Fractional, 2023 Despite the fact the Laplace transform has an appreciable efficiency in solving many equations, it cannot be employed to nonlinear equations of any type.
Moa’ath N. Oqielat +5 more
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Entropy, 2015 In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method.
Linjun Wang, Xumei Chen
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Asymptotic Solutions of Time-Space Fractional Coupled Systems by Residual Power Series Method [PDF]
Discrete Dynamics in Nature and Society, 2017 This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral.
Wenjin Li, Yanni Pang
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Solutions of Time Fractional fKdV Equation Using the Residual Power Series Method
Cumhuriyet Science Journal, 2022 The fifth-order Korteweg-de Vries (fKdV) equation is a nonlinear model in various long wave physical phenomena. The residual power series method (RPSM) is used to gain the approximate solutions of the time fractional fKdV equation in this study.
Sevil Çulha Ünal
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