DIMSEMs - diagonally implicit single-eigenvalue methods for the numerical solution of stiff ODEs on parallel computers (Q1371964)

The authors present a class of generalized linear methods which are suitable for the solution of stiff ordinary differential equations (ODEs) on parallel computers. The methods are similar to the DIMSIMs of \textit{J. C. Butcher} [World Sci. Ser. Appl. Anal. 2, 99-111 (1993; Zbl 0834.65059)]. \(A\)-stable DIMSEMs of order 2-6 are derived as well as an \(L\)-stable class of methods which, however, does not possess the single eigenvalue property. A variable stepsize implementation is presented and a comparison with the LSODE code is carried out.