QuantizedSystemSolver: A discontinuous ODE system solver in Julia.

Contemporary engineering systems, such as electrical circuits, mechanical systems with shocks, and chemical reactions with rapid kinetics, are often characterized by dynamics that can be modeled using stiff differential equations with events. Stiffness typically arises in these systems due to the presence of both rapidly changing and slowly changing components. This stiffness requires extremely small time steps to maintain stability when using traditional numerical integration techniques. Recently, quantization-based techniques have emerged as an effective alternative for handling such complex models. Methods like the Quantized State System (QSS) and the Linearly Implicit Quantized State System (LIQSS) offer promising results, particularly for large sparse stiff models. Unlike classic numerical integration methods, which update all system variables at each time step, the quantized approach updates individual system variables independently. Specifically, in quantized methods, each variable is updated only when its value changes by a predefined quantization level. Moreover, these methods are advantageous when dealing with discontinuous events. An event is a discontinuity where the state of the system abruptly changes at a specific point. Classic methods may struggle with events: They either undergo expensive iterations to pinpoint the exact discontinuity instance or resort to interpolating its location, resulting in unreliable outcomes. Therefore, this QSS strategy can significantly reduce computational effort and improve efficiency in large sparse stiff models with frequent discontinuities