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On General Linearly Implicit Quantized State System Methods
arXiv:2512.17855v1 Announce Type: new
Abstract: 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 current LIQSS methods while preserving their properties regarding stability, global error bound and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classic numerical integration algorithms is also analyzed.
Abstract: 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 current LIQSS methods while preserving their properties regarding stability, global error bound and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classic numerical integration algorithms is also analyzed.
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