We present a Krylov-W-code ROWMAP for the integration of stii initial value problems. It is based on the ROW-methods of the code ROS4 of Hairer and Wanner and uses Krylov techniques for the solutionâ€¦ (More)

We present a new class of explicit two-step peer methods for the solution of nonstiff differential systems. A construction principle for methods of order p = s, s the number of stages, with optimalâ€¦ (More)

Due to a two-step structure certain explicit peer methods with s stages have a natural parallel implementation on s processors. By the peer property all stages have essentially identical propertiesâ€¦ (More)

We consider explicit two-step peer methods for the solution of nonstiff differential systems. By an additional condition a subclass of optimally zero-stable methods is identified that isâ€¦ (More)

We consider W-methods and ROW-methods for stii initial value problems, where the stage equations are solved by Krylov techniques. By using a certain`multiple Arnoldi process' over all stages theâ€¦ (More)

Explicit parallel two-step peer methods use s stages with essentially identical properties. They are quite efficient in solving standard nonstiff initial value problems and may obtain a parallelâ€¦ (More)

Two-step W-methods are linearly implicit time-stepping methods using s external stages that may be processed in parallel. Methods with order s + 1 and stage order s exist. Appropriate generalizationsâ€¦ (More)

A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on theâ€¦ (More)

Peer two-step methods have been successfully applied to initial value problems for stiff and non-stiff ordinary differential equations both on parallel and sequential computers. Their essentialâ€¦ (More)