The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. in this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna.
General Linear Methods with external stages of different orders
VERMIGLIO, Rossana
1996-01-01
Abstract
The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. in this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna.File | Dimensione | Formato | |
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