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Articles

The method of fundamental solutions for the two-dimensional inverse Stefan problem

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Pages 112-129 | Received 04 Jul 2013, Accepted 17 Jul 2013, Published online: 02 Sep 2013

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W. B. da Silva, J. C. S. Dutra, C. E. P. Kopperschimidt, D. Lesnic & R. G. Aykroyd. (2021) Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters. Inverse Problems in Science and Engineering 29:13, pages 3322-3341.
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G. M. M. Reddy, M. Vynnycky & J. A. Cuminato. (2018) On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems. Inverse Problems in Science and Engineering 26:9, pages 1249-1279.
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Phalguni Nanda & Gujji Murali Mohan Reddy. (2022) Efficient numerical solution of one‐phase linear inverse Stefan and Cauchy–Stefan problems in two dimensions: A posteriori error control. Studies in Applied Mathematics 148:4, pages 1563-1585.
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A. Hajiollow, Y. Lotfi, K. Parand, A. H. Hadian, K. Rashedi & J. A. Rad. (2020) Recovering a moving boundary from Cauchy data in an inverse problem which arises in modeling brain tumor treatment: the (quasi)linearization idea combined with radial basis functions (RBFs) approximation. Engineering with Computers 37:3, pages 1735-1749.
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G. M. M. Reddy, P. Nanda, M. Vynnycky & J. A. Cuminato. (2021) An adaptive boundary algorithm for the reconstruction of boundary and initial data using the method of fundamental solutions for the inverse Cauchy–Stefan problem. Computational and Applied Mathematics 40:3.
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G.M.M. Reddy, M. Vynnycky & J.A. Cuminato. (2019) An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem. Journal of Computational and Applied Mathematics 349, pages 21-40.
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Saeed Sarabadan, Kamal Rashedi & Hojatollah Adibi. (2017) Boundary Determination of the Inverse Heat Conduction Problem in One and Two Dimensions via the Collocation Method Based on the Satisfier Functions. Iranian Journal of Science and Technology, Transactions A: Science 42:2, pages 827-840.
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Koya Sakakibara. (2017) Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions. Japan Journal of Industrial and Applied Mathematics 34:1, pages 177-228.
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Edyta Hetmaniok, Damian Słota & Adam Zielonka. (2015) Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem. Computers & Mathematics with Applications 69:4, pages 347-361.
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