Analytical Approximate Solutions of Systems of Multi-pantograph Delay Differential Equations Using Residual Power-series Method

Komashynska, Iryna; Al‐Smadi, Mohammed; Ateiwi, Ali Mahmud

doi:10.48550/arxiv.1611.05485

Cited by 3 publications

(5 citation statements)

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“…where k = 1,2,3,4, … , as shown in [2,3,6] and [12]. From the formulas ( 11) and ( 12), we write Res(x, t) = 0 and lim…”

Section: Analysis Of Rpsmmentioning

confidence: 99%

“…RPSM method have been used by several authors in various fields, such as Boussinesq-Burgers equations [16], fractional diffusion equations [14], fuzzy differential equations [1], fractional Burger types equations [13], time-fractional Fokker-Planck equations [20], time fractional nonlinear coupled Boussinesq-Burgers equations [15], nonlinear fractional KdV-Burgers equation [6], higher order initial value problems [2], for linear and nonlinear Lane-Emden equations [3], system of multipantograph differential equations [12], system of Fredhlom integral equations [11], time fractional Whitham-Broer-Kaup equations [19]], time fractional nonlinear gas dynamics equations [18], and is used for time fractional model of vibration equation [8]. Modeling and analysis of fractal-fractional partial differential equations for application to reaction-diffusion model [17] and analytic approximate solutions of diffusion equations arising in oil pollution have been studied [4].…”

Section: Introductionmentioning

confidence: 99%

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A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

Modanlı

Abdulazeez

Husien

2020

Numerical Methods Partial

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This article will give the residual power series method (RPSM) for solving pseudo hyperbolic partial differential equations with nonlocal conditions, RPSM is essentially based on general formula of Taylor series with residual error function. A new analytical solution is investigated. The analytical solution is designed to find the approximation solutions by RPSM and compare the obtained results from the current method with the exact solution that detects the precision, reliability, and rapid convergence of the proposed method. Finally at different times through the graphical representation of obtained results are given.

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“…where k = 1,2,3,4, … , as shown in [2,3,6] and [12]. From the formulas ( 11) and ( 12), we write Res(x, t) = 0 and lim…”

Section: Analysis Of Rpsmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

Modanlı

Abdulazeez

Husien

2020

Numerical Methods Partial

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“…The multi-pantograph delay differential (MP-DD) involving multiple singularities always difficult, grim, and challenging to solve numerically [1,2]. The MP-DD equations arise in various fields of applied physics and technology, such as astrophysics [3], electrodynamics [4], nonlinear dynamical models [5], electronic models [6], Hamiltonian systems [7], multimodal human computer interaction [8], catenary system [9], complex plane [10] and the problems related to engineering physics [11][12][13]. There are many powerful numerical techniques available in the literature to find the approximate results of the MP-DD equations.…”

Section: Introductionmentioning

confidence: 99%

“…There are many powerful numerical techniques available in the literature to find the approximate results of the MP-DD equations. To mention some of the techniques, Du and Geng [12] provided the approximate solutions using the reproducing kernel space. Yu [11] and Alipour et al [14] solved the MP-DD equation by applying the variational iteration (VI) scheme.…”

Section: Introductionmentioning

confidence: 99%

“…To mention some of the techniques, Du and Geng [12] provided the approximate solutions using the reproducing kernel space. Yu [11] and Alipour et al [14] solved the MP-DD equation by applying the variational iteration (VI) scheme. Jafari and Aminataei [15] suggested an approximation scheme to solve the MP-DD equations along with the differential neutral system.…”

Section: Introductionmentioning

confidence: 99%

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A design of novel Gudermannian neural networks for the nonlinear multi-pantograph delay differential singular model

Sabir,

Alhazmi

2023

Phys. Scr.

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In this paper, a new stochastic numerical platform through Gudermannian neural network (GNN) based intelligent computing solver (GNNICS) is accessible for solving the nonlinear singular multi-pantograph delay differential (MP-DD) systems. In GNNICS, Gudermannian kernel is exploited to construct the neural network models of differential operators with different neurons for the nonlinear system and hybrid computing via global genetic algorithm (GA) and local refinements with active set (AS), i.e., GNN-GAAS method. A fitness function with GNN models is formulated for solving the MP-DD equation and optimization of the design variables of the network is performed with GAAS. To investigate the performance of the designed GNNICS based on GNN-GAAS algorithm, three different variants of the MP-DD systems are used to assess the correctness, effectiveness, and robustness. The statistical investigations based on different performance metrics have been presented to authenticate the consistent accuracy, convergence, and stability of the designed GNN-GAAS algorithm.

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Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations

Khan

Tchier

et al. 2022

Journal of Function Spaces

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In this paper, the higher nonlinear problems of fractional advection-diffusion equations and systems of nonlinear fractional Burger’s equations are solved by using two sophisticated procedures, namely, the q-homotopy analysis transform method and the residual power series method. The proposed methods are implemented with the Caputo operator. The present techniques are utilised in a very comprehensive and effective manner to obtain the solutions to the suggested fractional-order problems. The nonlinearity of the problem was controlled tactfully. The numerical results of a few examples are calculated and analyzed. The tables and graphs are constructed to understand the higher accuracy and applicability of the current method. The obtained results that are in good contact with the actual dynamics of the given problem, which is verified by the graphs and tables. The present techniques require fewer calculations and are associated with a higher degree of accuracy, and therefore can be extended to solve other high nonlinear fractional problems.

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Analytical Approximate Solutions of Systems of Multi-pantograph Delay Differential Equations Using Residual Power-series Method

Cited by 3 publications

References 0 publications

A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

A design of novel Gudermannian neural networks for the nonlinear multi-pantograph delay differential singular model

Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations

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