The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A general class of two-step Runge-Kutta methods for ordinary differential equations
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Explicit two-step peer methods
Computers & Mathematics with Applications
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
Parameter optimization for explicit parallel 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
Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation
Journal of Computational and Applied Mathematics
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The so-called two-step peer methods for the numerical solution of Initial Value Problems (IVP) in differential systems were introduced by R. Weiner, B.A. Schmitt and coworkers as a tool to solve different types of IVPs either in sequential or parallel computers. These methods combine the advantages of Runge-Kutta (RK) and multistep methods to obtain high stage order and therefore provide in a natural way a dense output. In particular, several explicit peer methods have been proved to be competitive with standard RK methods in a wide selection of non-stiff test problems. The aim of this paper is to propose an alternative procedure to construct families of explicit two step peer methods in which the available parameters appear in a transparent way. This allows us to obtain families of fixed stepsize s stage methods with stage order 2s-1, which provide dense output without extra cost, depending on some free parameters that can be selected taking into account the stability properties and leading error terms. A study of the extension of these methods to variable stepsize is also carried out. Optimal s stage methods with s=2,3 are derived.