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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 59, 2011 - Issue 10
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Original Articles

Homotopy Perturbation Method for Solving the Two-Phase Inverse Stefan Problem

Damian Słota Institute of Mathematics, Silesian University of Technology, Gliwice, PolandCorrespondence[email protected]
Pages 755-768 | Received 09 Sep 2010, Accepted 18 Feb 2011, Published online: 31 May 2011

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Tao Liu & Songshu Liu. (2018) Identification of diffusion parameters in a non-linear convection–diffusion equation using adaptive homotopy perturbation method. Inverse Problems in Science and Engineering 26:4, pages 464-478.
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Edyta Hetmaniok, Damian Słota & Adam Zielonka. (2014) Experimental Verification of Selected Artificial Intelligence Algorithms Used for Solving the Inverse Stefan Problem. Numerical Heat Transfer, Part B: Fundamentals 66:4, pages 343-359.
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M. Vynnycky & S.L. Mitchell. (2013) On the Accuracy of a Finite-Difference Method for Parabolic Partial Differential Equations with Discontinuous Boundary Conditions. Numerical Heat Transfer, Part B: Fundamentals 64:4, pages 275-292.
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Tien-Mo Shih, Yingbin Zheng, Martinus Arie & Jin-Cheng Zheng. (2013) Literature Survey of Numerical Heat Transfer (2010–2011). Numerical Heat Transfer, Part A: Applications 64:6, pages 435-525.
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Dileep Singh Chauhan, Rashmi Agrawal & Priyanka Rastogi. (2012) Magnetohydrodynamic Slip Flow and Heat Transfer in a Porous Medium over a Stretching Cylinder: Homotopy Analysis Method. Numerical Heat Transfer, Part A: Applications 62:2, pages 136-157.
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Edyta Hetmaniok, Iwona Nowak, Damian Słota & Adam Zielonka. (2012) Determination of Optimal Parameters for the Immune Algorithm Used for Solving Inverse Heat Conduction Problems with and without a Phase Change. Numerical Heat Transfer, Part B: Fundamentals 62:6, pages 462-478.
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Articles from other publishers (32)

Tao Liu, Zijian Ding, Jiayuan Yu & Wenwen Zhang. (2023) Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method. Mathematics 11:12, pages 2642.
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Samat A. Kassabek & Durvudkhan Suragan. (2023) A heat polynomials method for the two-phase inverse Stefan problem. Computational and Applied Mathematics 42:3.
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Samat A. Kassabek & Durvudkhan Suragan. (2023) Two-phase inverse Stefan problems solved by heat polynomials method. Journal of Computational and Applied Mathematics 421, pages 114854.
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P. Nanda, G.M.M. Reddy & M. Vynnycky. (2022) Inverse two-phase nonlinear Stefan and Cauchy-Stefan problems: A phase-wise approach. Computers & Mathematics with Applications 123, pages 216-226.
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S. Bodaghi, A. Zakeri, A. Amiraslani & A. H. Salehi Shayegan. (2022) Discrete mollification in Bernstein basis and space marching scheme for numerical solution of an inverse two-phase one-dimensional Stefan problem. Numerical Algorithms 90:4, pages 1569-1592.
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Tao Liu. (2022) Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method. Chaos, Solitons & Fractals 158, pages 112007.
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Nataliya Gol'dman. (2019) On mathematical models with unknown nonlinear convection coefficients in one-phase heat transform processes. AIMS Mathematics 4:2, pages 327-342.
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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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. 2018. The Classical Stefan Problem. The Classical Stefan Problem 683 716 .
S.C. Gupta. 2018. The Classical Stefan Problem. The Classical Stefan Problem 311 663 .
Merey M. Sarsengeldin, Abdullah S. Erdogan, Targyn A. Nauryz & Hassan Nouri. (2017) An approach for solving an inverse spherical two-phase Stefan problem arising in modeling of electric contact phenomena. Mathematical Methods in the Applied Sciences.
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Tao Liu. (2016) A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations. Computers & Mathematics with Applications 71:7, pages 1519-1523.
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Edyta Hetmaniok, Damian Słota, Roman Wituła & Adam Zielonka. (2015) Solution of the one-phase inverse Stefan problem by using the homotopy analysis method. Applied Mathematical Modelling 39:22, pages 6793-6805.
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Smita Tapaswini, S. Chakraverty & Diptiranjan Behera. (2015) Numerical solution of the imprecisely defined inverse heat conduction problem. Chinese Physics B 24:5, pages 050203.
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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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Yang Yu, Xiaochuan Luo & Haijuan Cui. (2015) The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization. Mathematical Problems in Engineering 2015, pages 1-13.
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Y. Khan. (2014) Two-Dimensional Boundary Layer Flow of Chemical Reaction MHD Fluid over a Shrinking Sheet with Suction and Injection. Journal of Aerospace Engineering 27:5.
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Kamal Rashedi, Hojatollah Adibi, Jamal Amani Rad & Kourosh Parand. (2014) Application of meshfree methods for solving the inverse one-dimensional Stefan problem. Engineering Analysis with Boundary Elements 40, pages 1-21.
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S. Jafarmadar, B. Jalilpour, D. D. Ganji & H. Taghavifar. (2014) A Unified Model Considering Effects of Droplet Break-Up and Air Entrainment at the Initial Stage of Fuel Spray Penetration. Mathematical Problems in Engineering 2014, pages 1-11.
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Yasir Khan. (2013) A novel Laplace decomposition method for non-linear stretching sheet problem in the presence of MHD and slip condition. International Journal of Numerical Methods for Heat & Fluid Flow 24:1, pages 73-85.
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Yasir Khan & Habibolla Latifizadeh. (2013) Application of new optimal homotopy perturbation and Adomian decomposition methods to the MHD non-Newtonian fluid flow over a stretching sheet. International Journal of Numerical Methods for Heat & Fluid Flow 24:1, pages 124-136.
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Edyta Hetmaniok, Damian Słota & Adam Zielonka. (2013) Experimental verification of immune recruitment mechanism and clonal selection algorithm applied for solving the inverse problems of pure metal solidification. International Communications in Heat and Mass Transfer 47, pages 7-14.
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N. L. Gol’dman. (2013) One-phase inverse Stefan problems with unknown nonlinear sources. Differential Equations 49:6, pages 680-687.
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N. L. Gol’dman. (2013) Uniqueness classes of solutions of two-phase coefficient inverse Stefan problems. Doklady Mathematics 87:2, pages 205-210.
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Edyta Hetmaniok, Iwona Nowak, Damian Słota & Roman Wituła. (2013) A study of the convergence of and error estimation for the homotopy perturbation method for the Volterra–Fredholm integral equations. Applied Mathematics Letters 26:1, pages 165-169.
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Mehdi Akbarzade & Yasir Khan. (2012) Nonlinear Dynamic Analysis of Conservative Coupled Systems of Mass-Spring via the Analytical Approaches. Arabian Journal for Science and Engineering 38:1, pages 155-162.
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Bogdan Căruntu & Constantin Bota. (2012) Approximate polynomial solutions for nonlinear heat transfer problems using the squared remainder minimization method. International Communications in Heat and Mass Transfer 39:9, pages 1336-1341.
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Sunil Kumar, Yasir Khan & Ahmet Yildirim. (2011) A mathematical modeling arising in the chemical systems and its approximate numerical solution. Asia-Pacific Journal of Chemical Engineering 7:6, pages 835-840.
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Edyta Hetmaniok, Damian Słota & Roman Wituła. (2012) Convergence and error estimation of homotopy perturbation method for Fredholm and Volterra integral equations. Applied Mathematics and Computation 218:21, pages 10717-10725.
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N. L. Gol’dman. (2012) Uniqueness of determination of a source function in a quasilinear inverse stefan problem with final observation. Doklady Mathematics 85:3, pages 406-410.
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Edyta Hetmaniok, Iwona Nowak, Damian Słota & Roman Wituła. (2012) Application of the homotopy perturbation method for the solution of inverse heat conduction problem. International Communications in Heat and Mass Transfer 39:1, pages 30-35.
Crossref
Edyta Hetmaniok, Damian Słota, Adam Zielonka & Roman Wituła. 2012. Swarm and Evolutionary Computation. Swarm and Evolutionary Computation 249 257 .

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