**6. Conclusions**

A numerical method to estimate the temperature u x, t ð Þ and the coefficient *q*ð Þ x is proposed for an IHCP and the following results are obtained.

1.The present study, successfully applies the numerical method involving the Levenberg-Marquardt algorithm in conjunction with the Galerkin finite element method to an IHCP.

2.From the illustrated example it can be seen that the proposed numerical method is efficient and accurate to estimate the temperature u x, t ð Þ and the coefficient *q*ð Þ x .

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