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A new spectral collocation method for solving Bratu-type equations using Genocchi polynomials

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Abstract

In this paper, we have introduced a new Genocchi polynomial approximation method for solving Bratu-type equations arising in Engineering. With the help of Genocchi operational matrices of derivatives, the nonlinear differential equations are converted in to a system of algebraic equations. To the best of our knowledge until now there is no rigorous Genocchi spectral solution has been reported for the above model. The generalization of the Bratu-type models has led to the variety of Engineering applications such as radiative heat transfer, thermal reaction, chemical reactor theory and nanotechnology. Convergence and error analyses of the proposed method is also discussed. The power of the manageable method is confirmed. Finally, we have given a few examples to demonstrate the validity and applicability of the proposed spectral method. The obtained numerical results are compared with the Adomian decomposition method, Laplace transform method, genetic algorithm, perturbation-iteration algorithm, Artificial neural network and B-Spline method. Satisfactory agreement with the computational methods is observed.

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Acknowledgements

The authors are grateful to the Naval Research Board (NRB), New Delhi for financial support (Project No.: NRB-447/SC/19-20). We also acknowledge SASTRA Deemed University, Thanjavur for extending infrastructure support to carry out the study. Our sincere thanks are due to Mr. Selvaganesan and Mr. Bharatwaja srinivasan, NSTL-Lab, Visakhapatnam for providing the experimental data.

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Authors and Affiliations

  1. Department of Mathematics, School of Arts, Science and Humanities (SASH), SASTRA Deemed University, Thanjavur, Tamilnadu, India

    G. Swaminathan & G. Hariharan

  2. Scientist ‘F’, Naval Science and Technological Laboratory (NSTL), Vigyan Nagar, Visakhapatnam, 530027, India

    V. Selvaganesan & S. Bharatwaja

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  1. G. Swaminathan
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  2. G. Hariharan
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  4. S. Bharatwaja
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Correspondence to G. Hariharan.

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Swaminathan, G., Hariharan, G., Selvaganesan, V. et al. A new spectral collocation method for solving Bratu-type equations using Genocchi polynomials. J Math Chem 59, 1837–1850 (2021). https://doi.org/10.1007/s10910-021-01264-0

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  • DOI: https://doi.org/10.1007/s10910-021-01264-0

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