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A new acceleration of variational iteration method for initial value problems

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  • Shirazian, Mohammad

Abstract

This paper is devoted to accelerating the variational iteration method (VIM) to solve a nonlinear initial value problem. For this purpose, the redundant calculations of the conventional VIM are removed, and the complex integration is evaluated recursively and quickly with a suitable numerical approximation. The convergence of the proposed method is proven, and an efficient implementation algorithm is presented. This method is successfully applied to solve three applied equations, including the Riccati equation, the Lane–Emden equation, and the SIR epidemic model with a constant vaccination rate. Numerical simulations show that this improvement has significantly increased the method’s speed and enlarged its convergence region.

Suggested Citation

  • Shirazian, Mohammad, 2023. "A new acceleration of variational iteration method for initial value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 246-259.
    • Handle: RePEc:eee:matcom:v:214:y:2023:i:c:p:246-259
    DOI: 10.1016/j.matcom.2023.07.002
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    References listed on IDEAS

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    1. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    2. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Piccirillo, Vinicius, 2021. "Nonlinear control of infection spread based on a deterministic SEIR model," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    5. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    6. Luo, Xilin & Duan, Huiming & He, Leiyuhang, 2020. "A Novel Riccati Equation Grey Model And Its Application In Forecasting Clean Energy," Energy, Elsevier, vol. 205(C).
    7. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.
    8. Lal, Shyam & Kumari, Priya, 2021. "Approximation of functions with bounded derivative and solution of Riccati differential equations by Jacobi wavelet operational matrix," Applied Mathematics and Computation, Elsevier, vol. 394(C).
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