Matrix-free methods for stiff systems of ODE's
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs
Applied Numerical Mathematics - Special issue on time integration
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
Design, analysis and testing of some parallel two-step W-methods for stiff systems
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
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)
On the construction of restricted-denominator exponential W-methods
Journal of Computational and Applied Mathematics
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
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
Partially implicit peer methods for the compressible Euler equations
Journal of Computational Physics
Global error estimation and control in linearly-implicit parallel two-step peer W-methods
Journal of Computational and Applied Mathematics
Linearly implicit peer methods for the compressible Euler equations
Applied Numerical Mathematics
Peer methods for the one-dimensional shallow-water equations with CWENO space discretization
Applied Numerical Mathematics
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Parallel two-step W-methods are linearly-implicit integration methods where the s stage values can be computed in parallel. In this paper we consider a new class of two-step W-methods with s peer variables having almost identical characteristics. We discuss different types of such methods with order and stage order s - 1 or s and favourable stability properties. The new methods are more robust with respect to stepsize changes since they possess optimal damping at infinity. Numerical comparisons on a shared memory computer show the efficiency of the methods in combination with Krylov-techniques for MOL-systems.