volume | PIER Journals

Abstract

The positive-definite stability analysis (PDSA) is presented as a technique complementary to the companion-matrix stability analysis (CMSA). The PDSA is used to analyze the stability of marching-on-in-time (MOT) schemes. The heart of the PDSA is formed by the analysis on particular linear combinations of interaction matrices from an MOT scheme, which are assumed to be real-valued. If these are all positive definite, then the PDSA guarantees the stability of the scheme. The PDSA can be of a lower complexity than the full CMSA. The construction of the PDSA is shown and applied to two numerical examples.

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Mr. Petrus Wilhelmus Nicolaas (Pieter) Van Diepen

Prof. Martijn Constant van Beurden

Mr. Roeland Johannes Dilz