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
Order conditions for two-step Runge-Kutta methods
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Applied numerical linear algebra
Applied numerical linear algebra
Order Conditions for General Two-Step Runge--Kutta Methods
SIAM Journal on Numerical Analysis
Construction of two-step Runge--Kutta methods with large regions of absolute stability
Journal of Computational and Applied Mathematics
Algebraically stable diagonally implicit general linear methods
Applied Numerical Mathematics
Two-step Runge-Kutta Methods with Quadratic Stability Functions
Journal of Scientific Computing
Two-step Runge-Kutta Methods with Quadratic Stability Functions
Journal of Scientific Computing
Two-step diagonally-implicit collocation based methods for Volterra Integral Equations
Applied Numerical Mathematics
Numerical search for algebraically stable two-step almost collocation methods
Journal of Computational and Applied Mathematics
Construction of algebraically stable DIMSIMs
Journal of Computational and Applied Mathematics
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We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q=p or q=p-1. The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.