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International Journal of Computer Mathematics Volume 78, 2001 - Issue 2
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Original Articles

The iterative transformation method: numerical solution of one-dimensional parabolic moving boundary problems

Riccardo Fazio Department of Mathematics, University of Messina, Salita Sperone, Messina, 31, 98166, Italy E-mail: [email protected]
Pages 213-223 | Received 25 Apr 2000, Published online: 11 Jul 2012

Citations (15)

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Riccardo Fazio & Salvatore Iacono. (2010) On the moving boundary formulation for parabolic problems on unbounded domains. International Journal of Computer Mathematics 87:1, pages 186-198.
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Articles from other publishers (14)

Riccardo Fazio. (2022) A non-iterative transformation method for boundary-layer with power-law viscosity for non-Newtonian fluids. Calcolo 59:4.
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Tingyue Li, Dinghua Xu & Qifeng Zhang. (2021) High-order compact schemes for semilinear parabolic moving boundary problems. Applied Numerical Mathematics 161, pages 452-468.
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Riccardo Fazio. (2020) A non‐iterative transformation method for an extended Blasius problem. Mathematical Methods in the Applied Sciences 44:2, pages 1996-2001.
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Riccardo Fazio. (2020) Scaling invariance theory and numerical transformation method: A unifying framework. Applications in Engineering Science 4, pages 100024.
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Riccardo Fazio. (2019) The iterative transformation method. International Journal of Non-Linear Mechanics 116, pages 181-194.
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Riccardo Fazio. (2015) The iterative transformation method for the Sakiadis problem. Computers & Fluids 106, pages 196-200.
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W. Elson, C. Scheffer, K.H. Dellimore, P.R. Fourie & A.R. Coetzee. (2014) Development of an intravenous oxygenator using microbubbles. Development of an intravenous oxygenator using microbubbles.
Riccardo Fazio. (2013) Scaling invariance and the iterative transformation method for a class of parabolic moving boundary problems. International Journal of Non-Linear Mechanics 50, pages 136-140.
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Riccardo Fazio. (2013) Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension. Computers & Fluids 73, pages 202-209.
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Wan-Rong Cao & Zhi-Zhong Sun. (2010) Maximum norm error estimates of the Crank–Nicolson scheme for solving a linear moving boundary problem. Journal of Computational and Applied Mathematics 234:8, pages 2578-2586.
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Riccardo Fazio & Salvatore Iacono. (2010) On the equivalence of non-iterative transformation methods based on scaling and spiral groups. Mathematical Methods in the Applied Sciences 33:5, pages 585-591.
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Asai Asaithambi. (2007) Numerical solution of Stefan problems using automatic differentiation. Applied Mathematics and Computation 189:1, pages 943-948.
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Y Lu, K.H Parker & W Wang. (2006) Effects of osmotic pressure in the extracellular matrix on tissue deformation. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364:1843, pages 1407-1422.
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A.A. Salama & H.Z. Zidan. (2006) Fourth-Order Schemes of Exponential Type for Singularly Perturbed Parabolic Partial Differential Equations. Rocky Mountain Journal of Mathematics 36:3.
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