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Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method

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Abstract

In this paper, we consider the coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. First, we utilize systems of Volterra integral forms of the Lane–Emden equations and derive the modified recursion scheme for the components of the decomposition series solutions. The numerical results display that the Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. The error analysis of the sequence of the analytic approximate solutions can be performed by using the error remainder functions and the maximal error remainder parameters, which demonstrate an approximate exponential rate of convergence.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Nos. 11201308; 11171295) and the Innovation Program of Shanghai Municipal Education Commission (No. 14ZZ161).

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Author notes

  1. Jun-Sheng Duan

    Present address: School of Sciences, Shanghai Institute of Technology, Shanghai, 201418, People’s Republic of China

Authors and Affiliations

  1. 316 S. Maple St., Hartford, MI, 49057-1225, USA

    Randolph Rach

  2. School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, 526061, Guang Dong, People’s Republic of China

    Jun-Sheng Duan

  3. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

Authors
  1. Randolph Rach
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  2. Jun-Sheng Duan
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  3. Abdul-Majid Wazwaz
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Corresponding author

Correspondence to Jun-Sheng Duan.

Appendix: MATHEMATICA code generating Table 1 and Fig. 4

Appendix: MATHEMATICA code generating Table 1 and Fig. 4

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Rach, R., Duan, JS. & Wazwaz, AM. Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. J Math Chem 52, 255–267 (2014). https://doi.org/10.1007/s10910-013-0260-6

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  • DOI: https://doi.org/10.1007/s10910-013-0260-6

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