The Modified Polynomial Expansion Method for Solving the Inverse Heat Source Problems

Abstract

This article is aimed to reconstruct a time-dependent heat source for a one-dimensional heat conduction equation. The extra measurement data are used to transform the original equation into a homogeneous equation with three-point boundary conditions. Then the modified polynomial expansion method is developed to deal with the resulting three-point boundary-value problem. By considering the characteristic length, the modified polynomial expansion method can obtain a convergent series solution and improve the stability of the algorithm. The accuracy and efficiency of the present method are validated by comparing the estimating results with those of designed examples even under noisy measurement data.

Acknowledgments

The authors highly appreciate the grant from the National Science Council, Taiwan, under project number NSC 99-2221-E-019-053-MY3.