Two Kinds Of Wavelet Approximation Methods For Sloving The Backward Heat Conduction Problem

The backward heat conduction in time is the problem that a temperature distri-bution at t<T is reconstructed from the temperature data u(x,T)=gr(x)at a fixed time t=T>0 in a heat conduction body.The problem is a typical ill-posed problem,i.e.a small perturbation on gT(·)can cause great changes in the solution.Therefore,it needs special regularization method to solve the problem.We propose a wavelet shrinkage and the wavelet Galerkin regularization method to obtain the stable numerical solutions for this problem,respectively.At the same time,the er-ror estimates between the regularization approximation solution and exact solution under a prior parameter choice rule are given,which proves the methods converge at high level resolution.Finally,several examples are conducted to illustrated the effectiveness of the two regularization methods.