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http://dx.doi.org/10.14317/jami.2022.675

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)
Publication Information
Journal of applied mathematics & informatics / v.40, no.3_4, 2022 , pp. 675-694 More about this Journal
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
Radial basis function; heat equation; inverse problem; Boundary conditions;
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