The general a posteriori truncation method and its application to radiogenic source identification for the Helium production-diffusion equation

The purpose of the present paper is twofold: (i) to formulate the truncation method with a posteriori parameter choice rule in a uniform framework that can be adapted to solve a kind of linear inverse problems for which the solution can be represented by the eigensystem; (ii) to apply the a posteriori truncation method to the radiogenic source identification for the Helium production-diffusion equation, which is closely connected to the Helium isotopes dating as one method of the low temperature thermochronometry, the specific rate of convergence between the regularized solution and the exact solution is calculated, and numerical examples shed light on the efficiency and accuracy of the proposed method.