caa a22 4500 465751571 CHVBK 20180323111835.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF02250635 doi (NATIONALLICENCE)springer-10.1007/BF02250635 Numerical solution for the one-phase Stefan problem by Piecewise constant approximation of the interface [Elektronische Daten] [F. Sartoretto, R. Spigler] Numerische Lösung des Ein-Phasen Stefan Problems durch stückweise konstante Approximation der Interphase The classical one-phase one-dimensional Stefan problem is numerically solved on rectangles,R j , of increasing size controlled by the Stefan condition. This approach is based on a scheme introduced by E. Di Benedetto and R. Spigler in 1983. The practical implementation rests on the representation viathermal potentials of the solutionu j (x, t) to the heat equation inR j . The quantityu x j (x j ,jΔt) which determines the (j+1)-th rectangle is evaluatedanalytically by solving explicitly an integral equation. The solution inR j+1 is then obtained bynumerically evaluating a further integral expression. The algorithm is tested by solving two problems whose solution is explicitly known. Convergence, stability and convergence rate as Δx→0, Δt→0 have been tested and plots are shown. Springer-Verlag, 1990 Stefan problem nationallicence boundary integral methods nationallicence front tracking of the free boundary nationallicence numerical solution of free boundary problems nationallicence Sartoretto F. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Belzoni, 7, I-35131, Padova, Italy aut Spigler R. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Belzoni, 7, I-35131, Padova, Italy aut Computing Springer-Verlag 45/3(1990-09-01), 235-249 0010-485X 45:3<235 1990 45 607 https://doi.org/10.1007/BF02250635 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02250635 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sartoretto F. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Belzoni, 7, I-35131, Padova, Italy aut NATIONALLICENCE 700 1- Spigler R. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Belzoni, 7, I-35131, Padova, Italy aut NATIONALLICENCE 773 0- Computing Springer-Verlag 45/3(1990-09-01), 235-249 0010-485X 45:3<235 1990 45 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer