We introduce the truncation method for solving a backward heat conduction problem. For this method, we give the stability analysis with new error estimates. Meanwhile, we investigate the roles of regularization parameters in these two methods. These estimates prove that our method is effective. 2000 Mathematics Subject Classification: 35K05, 35K99, 47J06, 47H10..

the present study is concerned with optimal shape determination of inhomogeneous and temperature dependent domains under steady state heat conduction. such situations are important in many thermal design problems, especially in shape design of electronic components and chips. in the present paper, we formulate the shape optimization problem based on volume minimization of heat conductive materi...

Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

Mathematical model of direct and inverse problems is developed for the flat plate probe which is subjected to timedependent heat flux at one end, while the other end is kept insulated. The direct solution, which is concerned with determination of the temperature distribution in the probe, is developed using an approach based on the method of variation of parameters. The direct solution is used ...

‎in this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎for the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎it is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...

In the paper development a method for finding nonlinear heat-conducting characteristics of soil is being presented. Two-layer container complexes have been created, side faces which are thermally insulated so that 1D heat equation can be used. order not to solve boundary value problem with contact discontinuity and lose accuracy method’s solution, temperature sensor was placed at junction two m...

In many industrial applications one wants to determine the temperature on the surface of a body, where the surface itself is inaccessible to measurement [2, 4]. In this case it is necessary to determine surface temperature from a measured temperature history at a fixed location inside the body. This problem is called an inverse heat conduction problem (IHCP). In a one-dimensional setting, assum...

In this paper, the solution of one-phase inverse Stefan problem is presented. The problem consists of the reconstruction of the function which describes the distribution of temperature on the boundary, when the position of the moving interface is well-known. The proposed solution is based on the Adomian decomposition method and the least square method. (~) 2006 Elsevier Ltd. All rights reserved...

Purpose: of this paper: Aim of this paper is a presentation of the respectively new tool for solving the optimization problems, which is the Harmony Search algorithm in version slightly modified by the authors, used for identifying the thermal conductivity coefficient. Proposed approach is illustrated with an example confirming its usefulness for solving such kinds of problems. Design/methodolo...