Parallel 'Peer' two-step W-methods and their application to MOL-systems
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Optimizing locality and scalability of embedded Runge--Kutta solvers using block-based pipelining
Journal of Parallel and Distributed Computing
Linearly-implicit two-step methods and their implementation in Nordsieck form
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
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)
Explicit two-step peer methods
Computers & Mathematics with Applications
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
High-order linearly implicit two-step peer -- finite element methods for time-dependent PDEs
Applied Numerical Mathematics
Parameter optimization for explicit parallel peer two-step methods
Applied Numerical Mathematics
Rosenbrock-type 'Peer' two-step methods
Applied Numerical Mathematics
Implicit parallel peer methods for stiff initial value problems
Applied Numerical Mathematics
Linearly-implicit two-step methods and their implementation in Nordsieck form
Applied Numerical Mathematics
On the derivation of explicit two-step peer methods
Applied Numerical Mathematics
Global error estimation and control in linearly-implicit parallel two-step peer W-methods
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
On algebraic stability of general linear methods and peer methods
Applied Numerical Mathematics
Peer methods for the one-dimensional shallow-water equations with CWENO space discretization
Applied Numerical Mathematics
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
Adaptive ODE solvers in extended Kalman filtering algorithms
Journal of Computational and Applied Mathematics
Local and global error estimation and control within explicit two-step peer triples
Journal of Computational and Applied Mathematics
A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems
Journal of Computational and Applied Mathematics
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A new class of methods for the solution of stiff initial value problems is introduced that is parallel by design. It has a two-step character and propagates s different "peer" solution variables with essentially identical characteristics from step to step. The main work lies in the solution of s independent linear stage equations which may be solved in parallel. Convergence of order s-1 and stability for general stepsize sequences are proved. Conditions for order s and stronger stability criteria are addressed as well. Promising methods up to order 7 are identified by numerical tests with some widely used stiff test problems. Some of these are competitive with existing software even in sequential computations.