Journal ArticleDOI
On a free interface problem for linear ordinary differential equations and the one-phase Stefan problem
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TLDR
In this article, a numerical method for the solution of the one-phase Stefan problem is discussed, which converges to the solution with decreasing time increments, provided the proper algorithm is chosen for integrating the initial value problems.Abstract:
A numerical method for the solution of the one-phase Stefan problem is discussed. By discretizing the time variable the Stefan problem is reduced to a sequence of free boundary value problems for ordinary differential equations which are solved by conversion to initial value problems. The numerical solution is shown to converge to the solution of the Stefan problem with decreasing time increments. Sample calculations indicate that the method is stable provided the proper algorithm is chosen for integrating the initial value problems.read more
Citations
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Journal ArticleDOI
Randomization and the American Put
TL;DR: In this paper, a semi-explicit approximation for American option values in the Black Scholes model was proposed, based on randomization, which yields an approximation that is both accurate and computationally efficient.
Journal ArticleDOI
A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
Journal ArticleDOI
Numerical computation of the free boundary for the two-dimensional Stefan problem by space-time finite elements
R Bonnerot,P Jamet +1 more
TL;DR: In this article, a finite element method for the numerical solution of the two-dimensional Stefan problem is described, where at each time step, the free boundary is approximated by a polygonal line whose vertices coincide with triangulation nodes.
Journal ArticleDOI
Multidimensional Stefan Problems
TL;DR: In this paper, an implicit finite difference method for the multidimensional Stefan problem is discussed, where the classical problem with discontinuous enthalpy is replaced by an approximate Stefan problem with continuous piecewise linear enthpy.
Journal ArticleDOI
A second order finite element method for the one‐dimensional Stefan problem
R. Bonnerot,P Jamet +1 more
TL;DR: In this paper, a finite element method for the one-dimensional Stefan problem is described, where the elements are quadrilaterals of the space-time plane which are determined at each time-step in relation with the position of the free boundary.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
BookDOI
Differentialgleichungen : Lösungsmethoden und Lösungen
TL;DR: A molded plastic bowling pin incorporating a core extending the length of the pin substantially from its base to its head and constituted of a plurality of plastic core elements of varying sizes and shapes such that the composite pin incorporating the same meets the weight distribution standards set by the American Bowling Congress, and a shell having a substantially uniform thickness about the core elements and being integrally molded on and firmly bonded thereto.
Book
Ordinary Differential Equations
Garrett Birkhoff,Gian-Carlo Rota +1 more
TL;DR: In this paper, the authors propose an order of differential equations with constant coefficients for plane-autonomous systems and approximate solutions for linear Equations with Constant Coefficients with regular singular points.
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