The inverse problem of multi dimensional transient heat conduotion is studied with the least square method to determine the unknown boundary condition.The numerical tests show that this method has advantages of simple calculating, high precision and les effect of the measurement error.

A theoretical method called multiple-scattering expansion was proposed and developed by author in the previous works^[1].This method has a few advantages, such as,high accuracy, simplicity for calculations and wide valid region. This method has been applied to calculations for the impact ionization cross sections of H-atoms, and the results are in agreement with the experimental data very well^[2]. A detailed description for practical calculations based on this method is given in the present paper.

The analytical continuation method is used for evaluating efficiently and accuratyintegrals, such as∫₀^xr²χ₁(kr)χ₁,(k'r)χ_L(pr)dr, where χ₁(x) can be a spherical Bessel function j_l(x), or a spherical Neumanm function n_j(x). In particular, a practical program based on the method mintioned above has been made and its results show that the present method is very efficient and highly accurate.