Linearly implicit GARK schemes

Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization multiphysics systems is challenging, since different have levels stiffness characteristic time scales. The multimethod approach discretizes each process with an appropriate numerical method; the methods coupled appropriately such that overall solution has desired accuracy stability properties. authors developed general-structure additive Runge-Kutta (GARK) framework, which constructs multimethods based on schemes. This paper new GARK-ROS/GARK-ROW families linearly implicit Rosenbrock/Rosenbrock-W For ordinary differential equation models, we develop a general order condition theory for any number partitions, using exact or approximate Jacobians. We generalize two-way partitioned index-1 differential-algebraic equations. Applications framework include decoupled implicit, implicit/explicit, implicit/implicit methods. Practical GARK-ROS GARK-ROW schemes up four constructed.