Efficient general linear methods for ordinary differential equations

Numerical methods for ordinary differential equations have traditionallydeveloped along the lines of linear multistep methods and Runge–Kuttamethods. The ``general linear" formulation, which includes the standardmethods as special cases, while originally of mainly theoretical interest,has now shown itself to be capable of producing powerful newalgorithms.The aim of this proposal is to advance what is known about GLMsand to bring them to a level of development where they becomeviable options for a range of evolutionary problems.