Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MESHLESS AND HOMOTOPY PERTURBATION METHODS FOR ONE DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM WITH NEUMANN AND ROBIN BOUNDARY CONDITIONS

  • GEDEFAW, HUSSEN (Department of Mathematics, Samara University) ;
  • GIDAF, FASIL (Department of Mathematics, College of Natural Sciences, Wollo University) ;
  • SIRAW, HABTAMU (Department of Mathematics, College of Natural Sciences, Wollo University) ;
  • MERGIAW, TADESSE (Department of Mathematics, College of Natural Sciences, Wollo University) ;
  • TSEGAW, GETACHEW (Department of Mathematics, College of Natural Sciences, Wollo University) ;
  • WOLDESELASSIE, ASHENAFI (Department of Mathematics, Faculty of Natural and Computational Sciences, Woldia University) ;
  • ABERA, MELAKU (Kombolcha Institute of Technology, Wollo University) ;
  • KASSIM, MAHMUD (Department of Mathematics, Faculty of Natural and Computational Sciences, Woldia University) ;
  • LISANU, WONDOSEN (Department of Mathematics, Faculty of Natural and Computational Sciences, Woldia University) ;
  • MEBRATE, BENYAM (Department of Mathematics, College of Natural Sciences, Wollo University)
  • Received : 2021.07.19
  • Accepted : 2022.03.26
  • Published : 2022.05.30
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Abstract

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

Keywords

References

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