Algebraically stable general linear methods and the \(G\)-matrix
The authors discuss the algebraic stability of general linear methods, which governs long-time dynamics for dissipative systems and represents a stronger requirement than A-stability. The condition is reformulated in a modified form and connected to a branch of control theory concerned with the discrete algebraic Riccati equation. It is shown that the main condition for algebraic stability can be reformulated as an equation rather than an inequality with little loss of generality. For the construction of methods, the authors propose to first impose stability and subsequently satisfy the order conditions. The theoretical results are exploited to construct several new example methods with two steps and two stages.
scientific article; zbMATH DE number 5549597
scientific article