Alternating directions implicit integration in a general linear method framework

Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional equations. Classical ADI methods have order at most two, due the errors. Moreover, when time discretization stiff problems Runge-Kutta schemes, additional reduction may occur. This work proposes new partitioned General Linear Methods framework. allows construction high methods. Due their stage order, proposed can alleviate phenomenon seen with other schemes. Numerical experiments are shown provide further insight into accuracy, stability, applicability these