Abstract: In this paper the singular perturbation problem of linear algebraic equations with a small parameter is presented by an example in practice. The existence and uniqueness theorem of its solution is proved by the perturbation method and the estimation of error for its approximate solution is given. Finally, the example mentioned above explaining how to apply the theory to solve the stiff equations is shown.

Key words: semi-submerged body, fluid-structure interaction, finite element method, Arnoldi’s method