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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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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Alexandria Engineering Journal, 2023 The relaxation oscillator is a type of oscillator that is based on the nature of physical phenomena that tend to return to equilibrium after being distributed.
Geeta Arora +3 more
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Laplace Residual Power Series Method for Solving Three-Dimensional Fractional Helmholtz Equations
Symmetry, 2023 In the present study, the exact solutions of the fractional three-dimensional (3D) Helmholtz equation (FHE) are obtained using the Laplace residual power series method (LRPSM). The fractional derivative is calculated using the Caputo operator. First, we introduce a novel method that combines the Laplace transform tool and the residual power series ...
Wedad Albalawi +4 more
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Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method [PDF]
Complexity, 2017 We study the solution of fractional Fredholm integrodifferential equation. A modified version of the fractional power series method (RPS) is presented to extract an approximate solution of the model. The RPS method is a combination of the generalized fractional Taylor series and the residual functions.
Muhammed I. Syam
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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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Alexandria Engineering Journal, 2023 In this study, random ordinary differential equations obtained by randomly choosing the coefficients or initial conditions of the ordinary differential equations will be analyzed by the Residual Power Series Method. The initial conditions or coefficients of the equations will be converted to random variables with Normal, Gamma and exponential ...
Mehmet Merdan, Nihal Atasoy
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A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method [PDF]
Discrete Dynamics in Nature and Society, 2015 We implement a relatively new analytic iterative technique to get approximate solutions of differential algebraic equations system based on generalized Taylor series formula.
Khaled Moaddy +2 more
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MathematicsThis work introduces the General Residual Power Series Method (GRPSM) as a unified analytical framework encompassing the conventional Residual Power Series Method (RPSM) and its Laplace-like transform variants. By deriving a universal coefficient formula,
Pisamai Kittipoom, Jessada Tanthanuch
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Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method [PDF]
Mathematical Problems in Engineering, 2016 This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems inRn.
Xu, Fei +3 more
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