Application of New Iterative Method to Time Fractional Whitham–Broer–Kaup Equations

Nawaz, Rashid; Farid, Samreen; Shutaywi, Meshal; Shah, Zahir; Deebani, Wejdan

doi:10.3389/fphy.2020.00104

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…In Tables 1-4, the SDM results of this study are compared to methods that have been used in the past for Examples 1 and 2. Tese tables show that the simulation results using the methods described in [3,[26][27][28]40] are less accurate than the simulation results using the method under consideration. Tis shows that the method under consideration is efcient and reliable.…”

Section: Numerical Results and Discussionmentioning

confidence: 96%

“…( 2) transforms into a modifed Boussinesq (MB) equation, whereas when c 2 � 1 and c 1 ≠ 0, the system means an approximate long wave (ALW) equation. Similarly, the solution for the fractional order of WBK partial diferential equations was investigated using various analytical and numerical methods, such as the residual power series method [2], the Riccati subequation method [35], the exponential function method [36], the coupled fractional reduced diferential transform method (CFRDTM) [37], the q-homotopy analysis transform method (q-HATM) [38], the Laplace Adomian decomposition method (LADM) [3], the Yang decomposition method (YDM) [39], and the new iterative method (NIM) [40]. In 1980, Adomian presented the Adomian decomposition method (ADM), which is an efcient method for fnding numerical and explicit solutions to a large class of diferential equations representing physical problems.…”

Section: Introductionmentioning

confidence: 99%

“…Comparison of SDM solution of ξ(η, τ) with LADM[3] and NIM[40] of Example 2 with ε � 0.005, h � 0.1, c � 10, and ] � 1.…”

mentioning

confidence: 99%

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Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method

Ahmed

Elbadri

Hassan

et al. 2023

Journal of Mathematics

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In this paper, the coupled system of Whitham–Broer–Kaup equations of the Caputo fractional derivative (CFD) is studied using the Sumudu decomposition method (SDM). Using different dispersion relations, these equations are needed to describe the properties of waves in shallow water. The current investigation for the future scheme includes convergence and error analysis. We use two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to ensure its accuracy. The numerical simulation is carried out to ensure the accuracy of the future technique. The obtained numerical and graphical results are presented, and the proposed scheme is computationally very accurate and simple to study and solve fractionally coupled nonlinear complex phenomena encountered in science and technology.

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Section: Numerical Results and Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method

Ahmed

Elbadri

Hassan

et al. 2023

Journal of Mathematics

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show abstract

“…The appearance of problem (1) in various field of research and applications such as power flow equation, chemical equilibrium systems, compressive sensing, [1][2][3][4][5] and several others [6][7][8][9] have motivated several studies on effective methods for finding solutions to (1).…”

Section: Introductionmentioning

confidence: 99%

Another hybrid approach for solving monotone operator equations and application to signal processing

Abubakar

Ibrahim

Kura³

et al. 2022

Math Methods in App Sciences

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This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.

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“…We also use the NIM scheme which is based on the iterative principle of characteristics, introduced by Daftardar-Gejji and Jafari [22]. Recently, the application of NIM can be found in the literature specifically dealing with Klein-Gordon equations [23], fractional Whitham-Broer-Kaup (WBK) system [24], Fisher's equation [25], Cahn-Hillard equation [26], multidimensional wave equations [27], 1D Swift-Hohenberg equation [28], Falkner-Skan Equation [29], Jeffery-Hamel flow problem [30], Chemical kinetics equations [31,32], Lake pollution model [33] and many other problems. Stability analysis, Error bound, and Convergence analysis of NIM have been illustrated in Refs.…”

Section: Introductionmentioning

confidence: 99%

Accurate Numerical Treatment on a Stochastic SIR Epidemic Model with Optimal Control Strategy

et al. 2022

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In this paper, a numerical study has been undertaken on the susceptible-infected-recovered (SIR) epidemic model that encompasses the mechanisms of the evolution of disease transmission; a prophylactic vaccination strategy in the susceptible populations, depending on the infective individuals. We furnish numerical and graphical simulation combined with explicit series solutions of the proposed model using the New Iterative Method (NIM) and Modified New Iterative Method (MNIM). The analytic-numeric New Iterative Method failed to deliver accurate solution for the large time domain. A new reliable algorithm based on NIM, the coupling of the Laplace transforms, and the New Iterative method is called Modified New Iterative Method (MNIM) which is presented to enhance the validity domain of NIM techniques. The convergence analysis of the MNIM has also been illustrated. The simulation results show that the vaccination strategy can slow down the spread of the epidemic rapidly. Numerical results illustrate the excellent performance of the MNIM and show that the modified method is much more accurate than the NIM.

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Application of New Iterative Method to Time Fractional Whitham–Broer–Kaup Equations

Cited by 8 publications

References 16 publications

Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method

Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method

Another hybrid approach for solving monotone operator equations and application to signal processing

Accurate Numerical Treatment on a Stochastic SIR Epidemic Model with Optimal Control Strategy

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