Nordsieck representation of DIMSIMs


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Abstract

A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations.The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.

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