In this paper, an explicit boundary-type numerical procedure, including a constraint-type fictitious time integration method (FTIM) and two-point boundary solution of the Lie-group shooting (LGSM), is constructed to tackle nonlinear nonhomogeneous backward heat conduction problems (BHCPs). Conventional methods cannot effectively overcome instability solve inverse that lack initial conditions ta...

Free Boundary Problems (FBP) motivated several studies in the past due to their relevance in applications [1 − 4]. From the mathematical point of view FBP are initial/ boundary value problems with a moving boundary [5]. The motion of the boundary is unknown (free boundary) and has to be determined together with the solution of the given partial differential equation. As a consequence the soluti...

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In this article, we consider a Cauchy problem of heat equation, that is, determining the unknown temperature and heat flux at an inaccessible boundary from scattered temperature measurements on an accessible boundary or in some interior locations. This method is similar to the boundary control approach proposed by Leevan Ling and Tomoya Takeuchi in [1] where the authors considered a Cauchy prob...

Non-standard backward heat conduction problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we proposed a regularization strategy-central difference method to analysis the stability of the problem. Meanwhile, we investigate the function of the regularization parameter, two numerical implementations are described. Numerical exa...

This paper deals with transient non-linear heat conduction through the insulation wall of the tank for transportation of liquid aluminum. Tanks designed for this purpose must satisfy certain requirements regarding temperature of loading and unloading, during transport. Basic theoretical equations are presented, which describe the problem of heat conduction finite element analysis, starting from...

We define and analyze a linear transformation – the heat transform – that allows to map solutions of hyperbolic equations to solutions of corresponding parabolic equations. The inversion of this mapping can be used to transform an inverse problem for the heat equation to a similar problem for the wave equation. This work is motivated by problems of finding interfaces, boundaries and associated ...