The Journal of the Indian Mathematical Society

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Solving Uncertain Differential Equation with Fuzzy Boundary Conditions


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

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In this paper, a novel technique has been developed for solving a general linear dierential equation with fuzzy boundary conditions. The target has been to use the developed technique to solve in particular the radon transport (subsurface soil to buildings) equation with uncertain (fuzzy) boundary conditions. The fuzzy boundary condition has been described by a triangular fuzzy number (TFN). Corresponding results are presented in term of plots and are also compared with crisp ones.

Keywords

Advection, Diffusion, Fuzzy, Geometric, Radon.
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  • Moore, R. E., Kearfott, R. B., and Cloud, M. J, Introduction to interval analysis, Society for Industrial and Applied Mathematics (2009).

  • Bede, B., and Gal, S. G. . Almost periodic fuzzy-number-valued functions. Fuzzy Sets and Systems, 147(3)(2004), 385-403.

  • Gasilov, N., Amrahov, S. G., and Fatullayev, A. G. . A geometric approach to solve fuzzy linear systems of differential equations, arXiv preprint arXiv:0910.4307 (2009).

  • Kaleva, O. Fuzzy differential equations. Fuzzy sets and systems, 24(3)(1987), 301-317.

  • Behera, D., and Chakraverty, S. New approach to solve fully fuzzy system of linear equations using single and double parametric form of fuzzy numbers. Sadhana, 40(1)(2015),35-49.

  • Parandin, N. Numerical solution of fuzzy differential equations of nth order by Runge Kutta method, Neural Computing and Applications, 21(1)(2012), 347-355.

  • S. Tapaswini, S., and Chakraverty,S. New analytical method for solving n-th order fuzzy differential equations, Annals of Fuzzy Mathematics and Informatics. 8(2014), 231-244.

  • Chakraverty, S., Tapaswini, S. and Behera, D., Fuzzy Differential Equations and Applications for Engineers and Scientists, CRC Press Taylor and Francis Group, Boca Raton,United States, (2016).

  • Tapaswini, S., and Chakraverty, S. New Midpoint-based Approach for the Solution of n-th Order Interval Differential Equations, (2014).

  • Allahviranloo, T., Kiani, N. A., & Motamedi, N. Solving fuzzy differential equations by differential transformation method. Information Sciences, 179(7)(2009), 956-966.

  • Chalco-Cano, Y., and Rom´an-Flores, H. On new solutions of fuzzy differential equations. Chaos, Solitons & Fractals, 38(1)(2008), 112-119.

  • Chang, S. S., and Zadeh, L. A. On fuzzy mapping and control. IEEE Transactions on Systems, Man, and Cybernetics, (1)(1972), 30-34.

  • Khastan, A., Bahrami, F., and Ivaz, K. New results on multiple solutions for nthorder fuzzy differential equations under generalized differentiability. Boundary Value Problems, 2009(1), 395714.

  • Xu, J., Liao, Z., and Hu, Z. A class of linear differential dynamical systems with fuzzy initial condition, Fuzzy sets and systems, 158(21)(2007), 2339-2358.

  • Nazaroff, W. W. Radon transport from soil to air, Reviews of Geophysics, 30(2)(1992),137-160.

  • Kohl, T., Medici, F., and Rybach, L. Numerical simulation of radon transport from subsurface to buildings, Journal of applied geophysics, 31(1)(1994), 145-152.

  • Kozak, J. A., Reeves, H. W., and Lewis, B. A. Modeling radium and radon transport through soil and vegetation, Journal of contaminant hydrology, 66(3)(2003), 179-200.

  • Savovi´c, S., Djordjevich, A., and Risti´c, G. Numerical solution of the transport equation describing the radon transport from subsurface soil to buildings, Radiation protection dosimetry, 150(2)(2012), 213-216.

  • Telford, W. M. Radon mapping in the search for uranium,In Developments in Geophysical Exploration Methods—4, Springer Netherlands, (1983), 155-194.

  • Escobar, V. G., Tome, F. V., and Lozano, J. C.Procedures for the determination of 222-Rn exhalation and effective 226 Ra activity in soil samples, Applied radiation and Isotopes, 50(6)(1999), 1039-1047.

  • Schery, S. D., Holford, D. J., Wilson, J. L., and Phillips,F. M. The flow and Diffusion of radon isotopes in fractured porous media Part 2, Semi infinite media, Radiation Protection Dosimetry, 24(1-4)(1988), 191-197.


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  • Solving Uncertain Differential Equation with Fuzzy Boundary Conditions

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Authors

T. D. Rao
Department of Mathematics, National Institute of Technology Rourkela, Odisha-769008, India
S. Chakraverty
Department of Mathematics, National Institute of Technology Rourkela, Odisha-769008, India

Abstract


In this paper, a novel technique has been developed for solving a general linear dierential equation with fuzzy boundary conditions. The target has been to use the developed technique to solve in particular the radon transport (subsurface soil to buildings) equation with uncertain (fuzzy) boundary conditions. The fuzzy boundary condition has been described by a triangular fuzzy number (TFN). Corresponding results are presented in term of plots and are also compared with crisp ones.

Keywords


Advection, Diffusion, Fuzzy, Geometric, Radon.

References





DOI: https://doi.org/10.18311/jims%2F2019%2F18122