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Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis

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Abstract

We investigate the analytical and numerical solutions of the time-delayed Burgers equation, by applying the idea of commutative hypercomplex mathematics and the homotopy perturbation method. Moreover, we discuss at great length the convergence conditions of the homotopy perturbation Method (HPM) by using the Banach fixed point theory , which could provide a good iteration algorithm. Finally, we also give some numerical illustrations to the obtained results.

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Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

    Davood Rostamy & K. Karimi

  2. Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran

    Davood Rostamy

Authors
  1. Davood Rostamy
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  2. K. Karimi
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Correspondence to Davood Rostamy.

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Rostamy, D., Karimi, K. Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis. Numer Algor 58, 85–101 (2011). https://doi.org/10.1007/s11075-011-9448-7

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  • DOI: https://doi.org/10.1007/s11075-011-9448-7

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