scholarly journals Solution of one-dimensional moving boundary problem with periodic boundary conditions by variational iteration method

2009 ◽  
Vol 13 (2) ◽  
pp. 199-204 ◽  
Author(s):  
Rai Nath ◽  
Das Subir
Keyword(s):  
Boundary Conditions ◽  
Boundary Problem ◽  
Iteration Method ◽  
Periodic Boundary ◽  
Moving Boundary ◽  
Variational Iteration Method ◽  
Periodic Boundary Conditions ◽  
Moving Boundary Problem ◽  
One Dimensional ◽  
Variational Iteration

scholarly journals Variational iteration method to solve moving boundary problem with temperature dependent physical properties

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 229-239 ◽  
Author(s):  
Jitendra Singh ◽  
Kumar Gupta ◽  
Nath Rai
Keyword(s):  
Thermal Conductivity ◽  
Physical Properties ◽  
Specific Heat ◽  
Boundary Problem ◽  
Iteration Method ◽  
Moving Boundary ◽  
Variational Iteration Method ◽  
Moving Boundary Problem ◽  
Temperature Dependent ◽  
Variational Iteration

In this paper, variational iteration method is used to solve a moving boundary problem arising during melting or freezing of a semi infinite egion when physical properties (thermal conductivity and specific heat) of the two regions are temperature dependent. The Result is compared with result obtained by exact method (when thermal conductivity and specific heat in two regions are temperature independent) and semi analytical method (When thermal conductivity and specific heat are temperature dependent) and are in good agreement. We obtain the solution in the form of continuous functions. The method performs extremely well in terms of efficiency and simplicity and effective for solving the moving boundary problem.

scholarly journals Numerical study of one-dimensional Stefan problem with periodic boundary conditions

2013 ◽  
Vol 17 (5) ◽  
pp. 1453-1458
Author(s):  
Liang-Hui Qu ◽  
Feng Ling ◽  
Lin Xing
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Boundary Conditions ◽  
Stefan Problem ◽  
Periodic Boundary ◽  
Moving Boundary ◽  
Numerical Study ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Stefan Number

A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.

scholarly journals An approximate method for solving a melting problem with periodic boundary conditions

2014 ◽  
Vol 18 (5) ◽  
pp. 1679-1684
Author(s):  
Liang-Hui Qu ◽  
Lin Xing ◽  
Zhi-Yun Yu ◽  
Feng Ling ◽  
Jian-Guo Xu
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Moving Boundary ◽  
Analytic Solution ◽  
Functional Relation ◽  
Periodic Boundary Conditions ◽  
Approximate Analytic Solution ◽  
Infinite Domain ◽  
Effective Thermal Diffusivity ◽  
One Dimensional

An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compared with previous results in open literature.

Time-periodic solutions to the one-dimensional wave equation with periodic or anti-periodic boundary conditions

2007 ◽  
Vol 137 (2) ◽  
pp. 349-371 ◽  
Author(s):  
Shuguan Ji ◽  
Yong Li
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Boundary Conditions ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Dimensional Wave

This paper is devoted to the study of time-periodic solutions to the nonlinear one-dimensional wave equation with x-dependent coefficients u(x)ytt – (u(x)yx)x + g(x,t,y) = f(x,t) on (0,π) × ℝ under the periodic boundary conditions y(0,t) = y(π,t), yx(0,t) = yx(π,t) or anti-periodic boundary conditions y(0, t) = –y(π,t), yx[0,t) = – yx(π,t). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. Our main concept is that of the ‘weak solution’. For T, the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.

scholarly journals Global Attractors of Sixth Order PDEs Describing the Faceting of Growing Surfaces

2015 ◽  
Vol 28 (1) ◽  
pp. 49-67 ◽  
Author(s):  
M. D. Korzec ◽  
P. Nayar ◽  
P. Rybka
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Initial Conditions ◽  
Periodic Boundary Conditions ◽  
Global Attractors ◽  
Sixth Order ◽  
Two Dimensional ◽  
One Dimensional ◽  
Crystalline Surface ◽  
Dimensional Version

Abstract A spatially two-dimensional sixth order PDE describing the evolution of a growing crystalline surface h(x, y, t) that undergoes faceting is considered with periodic boundary conditions, as well as its reduced one-dimensional version. These equations are expressed in terms of the slopes $$u_1=h_{x}$$ u 1 = h x and $$u_2=h_y$$ u 2 = h y to establish the existence of global, connected attractors for both equations. Since unique solutions are guaranteed for initial conditions in $$\dot{H}^2_{per}$$ H ˙ p e r 2 , we consider the solution operator $$S(t): \dot{H}^2_{per} \rightarrow \dot{H}^2_{per}$$ S ( t ) : H ˙ p e r 2 → H ˙ p e r 2 , to gain our results. We prove the necessary continuity, dissipation and compactness properties.

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