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<p>This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using this idea, two novel sub-families of algorithms are designed that improve the performance of existing LIQSS methods while preserving their properties regarding stability, global error bounds and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classical numerical integration algorithms are also analyzed.</p>

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On general linearly implicit quantized state system methods

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Mariana Bergonzi,
  • Joaquín Fernandez,
  • Ernesto Kofman

摘要

This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using this idea, two novel sub-families of algorithms are designed that improve the performance of existing LIQSS methods while preserving their properties regarding stability, global error bounds and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classical numerical integration algorithms are also analyzed.