Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Implicit parallel peer methods for stiff initial value problems
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
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By definition algebraic stability of general linear methods is characterized by the existence of a weight matrix G leading to semi-definiteness of a 2x2 block test matrix depending on the coefficient matrices of the method. A congruence transformation is presented here reducing the number of places where G appears from 5 to 2 under assumptions satisfied by many methods from literature. A further reduction is possible to a test matrix depending on one single aggregated coefficient matrix P only. Simple sufficient and sharp necessary conditions on P are discussed. With these many algebraically stable implicit two-step peer methods with 3 stages and order 2 are constructed. Finally relations to Riccati equations and a generalized eigenvalue problem of Hill are discussed.