James Caldwell

Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions

Abstract A finite difference method is used to solve the one-dimensional Stefan problem with periodic Dirichlet boundary condition. The temperature distribution, the position of the moving boundary and its velocity are evaluated. It is shown that, for given oscillation frequency, both the size of the domain and the oscillation amplitude of the periodically oscillating surface temperature, strongly influence the temperature distribution and the boundary movement. Furthermore, good agreement between the present finite difference results and numerical results obtained previously using the nodal integral method is seen.

On the perturbation method for the Stefan problem with time-dependent boundary conditions

Abstract Perturbation methods are developed for Stefan problems with time-dependent boundary conditions. The methods are applied to melting of ice in the half-plane, outward spherical solidification and outward cylindrical solidification of a saturated liquid. The results are shown to compare well with those obtained by other numerical methods.

Physical parameters reconstruction of a free-free mass-spring system from its spectra

Consider a linear, n degree-of-freedom, free–free, vibratory system. Suppose that the system under consideration is a multiply connected system, in the sense that each of its concentrated masses may be connected through a linear spring to each of its other masses. Let

Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem

\lambda _1^{(i)} , \cdots ,\lambda _i^{(i)}

Numerical solutions of the Stefan problem by the enthalpy method and the heat balance integral method

, be the eigenvalues of the system in the case where

Application of Broyden's method to the enthalpy method for phase change problems

n - i

Study of a deterministic model in the theory of contagious disease

masses of the system are pinned to the ground. Suppose that for

Deterministic modelling in the theory of contagious disease

i = 1,2, \cdots ,n

Numerical solution of melting/solidification problems in cylindrical geometry

the sets

Numerical solution of Stefan problem with time-dependent boundary conditions by variable space grid method

\lambda _1^{(i)} , \cdots ,\lambda _i^{(i)}