Improving the modified linearly implicit quantized state system methods: step size, cycle detection, and linear approximation coefficient

The growing intricacy of contemporary engineering systems, typically reduced to differential equations, poses a difficulty in digitally simulating them. The linearly implicit quantized state system (LIQSS) provides a different method from traditional numerical integration techniques for tackling such problems. This method is effective in large sparse stiff systems and systems with frequent discontinuities. However, this method could be further improved. First, the algorithm can step through the solution analytically or through iterations. A comparison is presented in this article. Second, the intrinsic discrete behavior of this new method can cause oscillations that lead to small unnecessary simulation steps. A prior approach was made to detect and terminate these cycles. Different detection mechanisms are examined in this article. Third, a linear approximation was used. Its enhancement is also investigated in this work. Finally, the article provides which of these modifications improved the overall performance of some systems simulations using LIQSS order one.