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
High order algebraically stable multistep Runge-Kutta methods
SIAM Journal on Numerical Analysis
Diagonally-implicit multi-stage integration methods
Applied Numerical Mathematics
Applied Numerical Mathematics
Applied numerical linear algebra
Applied numerical linear algebra
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Algebraically stable diagonally implicit general linear methods
Applied Numerical Mathematics
Search for highly stable two-step Runge-Kutta methods
Applied Numerical Mathematics
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The class of general linear methods for ordinary differential equations combines the advantages of linear multistep methods (high efficiency) and Runge-Kutta methods (good stability properties such as A-, L-, or algebraic stability), while at the same time avoiding the disadvantages of these methods (poor stability of linear multistep methods, high cost for Runge-Kutta methods). In this paper we describe the construction of algebraically stable general linear methods based on the criteria proposed recently by Hewitt and Hill. We also introduce the new concept of @e-algebraic stability and investigate its consequences. Examples of @e-algebraically stable methods are given up to order p=4.