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This paper aims to solve an inverse heat conduction problem with only boundary value in a bounded domain, where the boundary data is given for x=0$x=0$. The solution is sought in the interval 0<x≤1$0< x\leq1$. The problem is seriously ill posed in the Hadamard sense. Using the Hölder inequality and some inequalities, a conditional stability is proved for this problem. A modified Tikhonov regularization method is proposed to recover the stability of the solution. An order optimal error estimate between the approximate solution and the exact solution is obtained with a suitable choice of regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of the proposed method.

A modified regularization method for an inverse heat conduction problem with only boundary value