ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs Original Research Article

We present a Krylov-W-code ROWMAP for the integration of stiff initial value problems. It is based on the ROW-methods of the code ROS4 of Hairer and Wanner and uses Krylov techniques for the solution of linear systems. A special multiple Arnoldi process ensures order p = 4 already for fairly low dimensions of the Krylov subspaces independently of the dimension of the differential equations. Numerical tests and comparisons with the multistep code VODPK illustrate the efficiency of ROWMAP for large stiff systems. Furthermore, the application to nonautonomous systems is discussed in more detail.