Multirate linearly-implicit GARK schemes

Abstract Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve system, according their dynamics, in order achieve increased computational efficiency. The stiff fast or slow, are best discretized with implicit base methods ensure numerical stability. To this end, linearly particularly attractive as they solve only linear systems equations at each step. This paper develops GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. conditions theory considers both exact and approximative Jacobians. effectiveness depends on coupling between slow computations; an array efficient strategies resulting analyzed. infinitesimal methods, that allow arbitrarily small micro-steps offer extreme flexibility, constructed. new unifying includes existing Rosenbrock(-W) particular cases, opens possibility develop classes highly effective integrators.