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1.
S.Y. Reutskiy 《Applied mathematics and computation》2011,217(23):9689-9701
The paper presents a new meshless numerical technique for solving one-dimensional problems with moving boundaries including the Stefan problems. The technique presented is based on the use of the delta-shaped functions and the method of approximate fundamental solutions (MAFS) firstly suggested for solving elliptic problems and for heat equations in domains with fixed boundaries. The numerical examples are presented and the results are compared with analytical solutions. The comparison shows that the method presented provides a very high precision in determining the position of the moving boundary even for a region that initially has zero thickness. 相似文献
2.
Summary In this paper we suggest the use of complete families of solutions of the heat equation for the numerical solution of the inverse Stefan problem. Our approach leads to linear optimization problems which can be established and solved easily. Convergence results are proved. In a final section the method is applied to some examples. 相似文献
3.
Yu. V. Zhernovoi 《Ukrainian Mathematical Journal》1993,45(8):1178-1185
New formulations of the inverse nonstationary Stefan problems are considered: (a) forx [0,1] (the inverse problem IP1; (b) forx [0, (t)] with a degenerate initial condition (the inverse problem IP). Necessary conditions for the existence and uniqueness of a solution to these problems are formulated. On the first phase {x [0, y(t)]{, the solution of the inverse problem is found in the form of a series; on the second phase {x [y(t), 1] orx [y(t), (t)]{, it is found as a sum of heat double-layer potentials. By representing the inverse problem in the form of two connected boundary-value problems for the heat conduction equation in the domains with moving boundaries, it can be reduced to the integral Volterra equations of the second kind. An exact solution of the problem IP is found for the self similar motion of the boundariesx=y(t) andx=(t).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1058–1065, August, 1993. 相似文献
4.
Antonio Fasano Mario Primicerio Shoshana Kamin 《Annali di Matematica Pura ed Applicata》1977,115(1):341-348
Sunto Si considera il problema di Stefan unidimensionale a due fasi e si dimostra l'esistenza di soluzioni classiche sotto ipotesi
minimali sui dati (continuità a tratti e limitatezza). Nelle stesse ipotesi si dimostra che tali soluzioni dipendono in modo
continuo dai dati, conseguendo un risultato che è più generale anche di quello noto per le soluzioni deboli.
Entrata in Redazione il 22 dicembre 1976.
Work partially supported by the Italian C.N.R. 相似文献
Entrata in Redazione il 22 dicembre 1976.
Work partially supported by the Italian C.N.R. 相似文献
5.
Although the numerical solution of one-dimensional phase-change, or Stefan, problems is well documented, a review of the most recent literature indicates that there are still unresolved issues regarding the start-up of a computation for a region that initially has zero thickness, as well as how to determine the location of the moving boundary thereafter. This paper considers the so-called boundary immobilization method for four benchmark melting problems, in tandem with three finite-difference discretization schemes. We demonstrate a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution that is often used, and is numerically second-order accurate in both time and space, a point that has been consistently overlooked for this type of moving-boundary problem. 相似文献
6.
We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (?T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost. 相似文献
7.
Gunter H. Meyer 《Applied mathematics and computation》1978,4(4):283-306
The numerical performance of some computer methods for heat transfer with change of phase is discussed. For one-dimensional problems the application of invariant imbedding to time-discretized problems is suggested. For some multidimensional problems an absorption of the phase transition process into the diffusion equation through the so-called enthalpy transformation is advocated. If this transformation is not applicable, a locally one-dimensional Gauss-Seidel-type front-tracking method coupled with invariant imbedding is effective. 相似文献
8.
G. I. Bizhanova 《Journal of Mathematical Sciences》2000,99(1):816-836
Three one-dimensional problems with free boundary for second order parabolic equations are considered, namely, the Florin, Muskat-Verigin, and Stefan problems. Existence and uniqueness theorems in the weighted Hölder spaces are established for these problems. Coercive estimates for solutions are found. Bibliography:44 titles. 相似文献
9.
Wiemin Han 《Mathematical and Computer Modelling》1991,15(12):67-76
A systematic analysis is given on asymptotic error expansions for numerical solutions of one-dimensional problems whose solutions are singular. Numerical examples show a great improvement on the accuracy of numerical solutions by using the Richardson extrapolation technique. 相似文献
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Two models for thermal stratification based on turbulent diffusion concepts are analysed and compared. The models by Henderson-Sellers; and by McCormick and Scavia, are shown to be equivalent at large values of the Richardson number, Ri. At small Ri, the simpler model reverts to specification of the turbulent diffusion as a constant value. This simplification is also demonstrated to be a realistic approximation only at low wind speeds and for deep lakes. By comparison of these model types, a (previously empirically defined by McCormick and Scavia) parameter β is related conceptually to the lake depth, H. 相似文献
12.
Rbert Horvth 《Applied Mathematical Modelling》2008,32(8):1570-1578
The preservation of the qualitative properties of physical phenomena in numerical models of these phenomena is an important requirement in scientific computations. In this paper, the numerical solutions of a one-dimensional linear parabolic problem are analysed. The problem can be considered as a altitudinal part of a split air pollution transport model or a heat conduction equation with a linear source term. The paper is focussed on the so-called sign-stability property, which reflects the fact that the number of the spatial sign changes of the solution does not grow in time. We give sufficient conditions that guarantee the sign-stability both for the finite difference and the finite element methods. 相似文献
13.
Numerical Algorithms - In this paper, a one-dimensional two-phase inverse Stefan problem is studied. The free surface is considered unknown here, which is more realistic from the practical point of... 相似文献
14.
In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size. 相似文献
15.
We compare the numerical solutions of three fractional partial differential equations that occur in finance. These fractional partial differential equations fall in the class of Lévy models. They are known as the FMLS (Finite Moment Log Stable), CGMY and KoBol models. Conditions for the convergence of each of these models is obtained. 相似文献
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18.
Zhu Ning 《高校应用数学学报(英文版)》1998,13(3):241-250
ANOTEONTHEBEHAVIOROFBLOW┐UPSOLUTIONSFORONE┐PHASESTEFANPROBLEMSZHUNINGAbstract.Inthispaper,thefolowingone-phaseStefanproblemis... 相似文献
19.
A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is extended for the purpose of solving one-phase ablation-type moving boundary problems; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. An important component of the work is the use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space. The analysis also determines that the ablation front initially moves as the time raised to the power 3/2; hence, it evolves considerably more slowly than the phase-change front in the classical Stefan problem with isothermal cooling. 相似文献
20.
B.K. Muite 《Journal of Computational and Applied Mathematics》2010,234(2):317-342
In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral space preconditioned Chebyshev tau, real space Chebyshev integration and spectral space Chebyshev integration methods are compared in the L2 and W2,2 norms when solving linear fourth order boundary value problems; and in the L∞([0,T];L2) and L∞([0,T];W2,2) norms when solving initial boundary value problems. We find that the best Chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space Chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to Fourier spectral discretization. 相似文献