[en] The multicomponent time-dependent diffusion with radioactive decay problem which arises in the study of high-temperature gas-cooled reactors fission product migration is solved in one-dimensional geometries. The spatial multicomponent diffusion operator is numerically represented by a conservative finite difference approximation. An analytic time-dependent solution is achieved using a matrix operator method. Comparisons of the analytic-numerical solution method with a variety of analytic solutions give excellent agreement. This solution technique has been incorporated into an algorithm for use in a computer code, DASH. The holdup of ⁹⁰Sr by graphite is calculated