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Modeling Radon Diffusion Equation by Using Fuzzy Polynomials in Galerkin’s Method

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Recent Advances in Applications of Computational and Fuzzy Mathematics

Abstract

Radon is a naturally occurring radioactive noble gas which emanates from rocks and soils during the radioactive decay of radium atom inside the material grains. Radon transport in soil pore is usually governed by the physical processes, namely diffusion. Solving the corresponding differential equation with uncertain (fuzzy) parameter is challenging. Accordingly, in this chapter a new technique based on fuzzy polynomials in Galerkin’s method has been proposed to solve the said uncertain differential equation (DE). The shape functions in the initial approximation have been taken as fuzzy polynomials which satisfy the given boundary conditions of the problem. The uncertainty in the DEs is taken in the boundary/initial conditions in fuzzy form. Different degrees of fuzzy polynomials are considered for the simulation. As such step-by-step procedure of the method has also been demonstrated. Obtained results are compared with their exact solutions (wherever possible) in order to demonstrate the validity and applicability of the method.

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Acknowledgements

The authors are thankful to Board of Research in Nuclear Sciences (BRNS), Mumbai, India (Grant Number: 36(4)/40/46/2014-BRNS), for the support and funding to carry out the present research work.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, Odisha, India

    T. D. Rao & Snehashish Chakraverty

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  1. T. D. Rao
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  2. Snehashish Chakraverty
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Correspondence to T. D. Rao .

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Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India

    Snehashish Chakraverty

  2. Research & Development Centre for Mathematical Modeling, Faculty of Science, University of Colombo, Colombo, Sri Lanka

    Sanjeewa Perera

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Rao, T.D., Chakraverty, S. (2018). Modeling Radon Diffusion Equation by Using Fuzzy Polynomials in Galerkin’s Method. In: Chakraverty, S., Perera, S. (eds) Recent Advances in Applications of Computational and Fuzzy Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1153-6_4

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  • DOI: https://doi.org/10.1007/978-981-13-1153-6_4

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  • Print ISBN: 978-981-13-1152-9

  • Online ISBN: 978-981-13-1153-6

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