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A predictor–corrector scheme for the improved Boussinesq equation

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  • Bratsos, A.G.

Abstract

An implicit finite-difference method based on rational approximants of second order to the matrix-exponential term in a three-time level recurrence relation has been proposed for the numerical solution of the improved Boussinesq equation already known from the bibliography. The method, which is analyzed for local truncation error and stability, leads to the solution of a nonlinear system. To overcome this difficulty a predictor–corrector (P–C) scheme in which the predictor is also a second order implicit one is proposed. The efficiency of the proposed method is tested to various wave packets and the results arising from the experiments are compared with the relevant ones known in the bibliography.

Suggested Citation

  • Bratsos, A.G., 2009. "A predictor–corrector scheme for the improved Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2083-2094.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2083-2094
    DOI: 10.1016/j.chaos.2007.09.083
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    References listed on IDEAS

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    1. Javidi, M. & Jalilian, Y., 2008. "Exact solitary wave solution of Boussinesq equation by VIM," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1256-1260.
    2. Inc, Mustafa, 2008. "New solitary wave solutions with compact support and Jacobi elliptic function solutions for the nonlinearly dispersive Boussinesq equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 792-798.
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    4. Abassy, Tamer A. & El-Tawil, Magdy A. & Saleh, Hassan K., 2007. "The solution of Burgers’ and good Boussinesq equations using ADM–Padé technique," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1008-1026.
    5. El-Wakil, S.A. & Elgarayhi, A. & Elhanbaly, A., 2006. "Exact periodic wave solutions for some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 1037-1044.
    6. Dai, Zhengde & Huang, Jian & Jiang, Murong & Wang, Shenghua, 2005. "Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1189-1194.
    7. Lesnic, D., 2006. "Blow-up solutions obtained using the decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 776-787.
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    1. Wongsaijai, B. & Oonariya, C. & Poochinapan, K., 2020. "Compact structure-preserving algorithm with high accuracy extended to the improved Boussinesq equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 125-150.

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