Numerical Solution Of A Class Of Non-standard Inverse Heat Conduction Problem

Inverse heat conduction problem is a serious ill-posed problem, namely the solution of problem does not depend continuously on the measured data, solving such problems is very difficult. Now for the standard inverse heat conduction prob-lem there are a lot of results, but for non-standard inverse heat conduction problem results are scarce. In this paper, with convection, non-standard inverse heat conduc-tion problem solution based on wavelet analysis and restore the data to understand the continuous dependence.Consider the following two kinds of determining the heat flux ux(x, t),0≤x< 1 non-standard inverse heat conduction problem. andAnalyse the problem ill-posedness,using wavelet analysis method to restore the continuous dependence of solutions on the data, And gives error estimates between the exact solution and the regularized solution.This article is divided into three sections. The first chapter introduces the non-standard inverse heat conduction problem of the background and significance, the current research status, and the difficulties of the research. The second chapter is to study some of the issues presented need to use the basic knowledge and theory, including improperly posed problems, regularization method, and wavelet analysis. The third chapter is the main part of the paper, it presented the mathematical model of the non-standard inverse heat conduction problem. Using wavelet analysis method to restore continuous dependence of solutions on data given error estimates.