A novel iterative method for solving chemical kinetics system

Chowdhury, Md. Sazzad Hossien; Ghosh, Indranil; Aznam, Suazlan Mt; Mawa, Shukranul

doi:10.1177/1461348421992610

Cited by 6 publications

(3 citation statements)

References 43 publications

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“…Daftardar-Gejji and Jafari [9] envisioned the New Iterative Method in order to solve fractional, ordinary and partial differential equations. Later, quite a few studies based on the New Iterative Method (NIM) was conducted when solving Nonlinear Integro-Differential Equations [10], Fokker-Planck Equation [11], Klein-Gordon equations [12], nonlinear functional equations [13], Falkner-Skan Equation [14], Jeffery-Hamel flow problem [15], Chemical kinetics equations [16,17], Lake pollution model [18] and many other problems. This method is also referred as the Daftardar-Jafari method (DJM) or Iterative method (IM).…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment on a Chaos Model of Fluid Flow Using New Iterative Method

Ghosh

Chowdhury²,

Aznam³

2022

ARFMTS

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This article treats analytically and numerically to the three dimensional Rössler system. The governing equations of the problem are derived from traditional Lorentz system of fluid mechanics to nonlinear ordinary differential equations (ODEs) for modelling. A semi-analytic solution is developed by using New Iterative Method (NIM) whereas the numerical solution is presented by Runge-Kutta order four (RK4) scheme. A comparative study of the analytical and numerical solutions are made. The results confirm clearly that the two methods coincide closely for both the chaotic and non-chaotic cases of the determined system. This observation would be helpful to apply NIM on nonlinear problems of fluid flow with different fluid parameters in future.

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Section: Introductionmentioning

confidence: 99%

Numerical Treatment on a Chaos Model of Fluid Flow Using New Iterative Method

Ghosh

Chowdhury²,

Aznam³

2022

ARFMTS

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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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“…Another prominent semianalytical technique which has been demonstrated to be a lot more straightforward and efficient than the abovementioned methods is called the new iterative method (NIM), first proposed by Varsha Daftardar-Gejji and Jafari [22] . Very recently, NIM was employed for solving Fokker-Planck equations [23], chemical kinetic equations [24], and Klein-Gordon equations [25]. Some other applications of the new iterative method (NIM) on nonlinear problems can be found in [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method

Ghosh

Chowdhury

Aznam

et al. 2021

Journal of Applied Mathematics

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Pollution has become an intense danger to our environment. The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input. In the present study, the new iterative method (NIM) was applied to the lake pollution model with three cases called impulse input, step input, and sinusoidal input for a longer time span. The main feature of the NIM is that the procedure is very simple, and it does not need to calculate any special type of polynomial or multipliers such as Adomian polynomials and Lagrange’s multipliers. Comparisons with the Adomian decomposition method (ADM) and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the NIM is a powerful alternative for differential equations providing more realistic series solutions that converge very rapidly in real physical problems.

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A novel iterative method for solving chemical kinetics system

Cited by 6 publications

References 43 publications

Numerical Treatment on a Chaos Model of Fluid Flow Using New Iterative Method

Numerical Treatment on a Chaos Model of Fluid Flow Using New Iterative Method

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

Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method

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