Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
A general class of two-step Runge-Kutta methods for ordinary differential equations
SIAM Journal on Numerical Analysis
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Rosenbrock-type 'Peer' two-step methods
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Implicit parallel peer methods for stiff initial value problems
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
Scalability and locality of extrapolation methods for distributed-memory architectures
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
On the derivation of explicit two-step peer methods
Applied Numerical Mathematics
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
Partially implicit peer methods for the compressible Euler equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Linearly implicit peer methods for the compressible Euler equations
Applied Numerical Mathematics
Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
Peer methods with improved embedded sensitivities for parameter-dependent ODEs
Journal of Computational and Applied Mathematics
Reprint of: Peer methods with improved embedded sensitivities for parameter-dependent ODEs
Journal of Computational and Applied Mathematics
Search for efficient general linear methods for ordinary differential equations
Journal of Computational and Applied Mathematics
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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 properties and we construct a class of zero-stable methods with order p=s in all stages. Two approaches are discussed for choosing the free parameters. In a certain subclass the stability polynomial depends only linearly on a new set of parameters and by employing tailored root locus bounds a linear program can be formulated and solved exactly for stable and accurate methods. The second approach uses Monte-Carlo simulation in a wider class of methods. The two approaches are compared in realistic numerical tests on a parallel computer.