The theoretical foundation of path-following methods is the performance analysis (damped) Newton step on class self-concordant functions. However, bounds available in literature and used design are not optimal. In this contribution we use optimal control theory to compute length method functions, as a function initial decrement, resulting worst-case decrease decrement. exact expressed terms sol...

To date, Lagrangian mass-transfer-based interacting particle methods have been shown to be rigorous and capable of modeling a diverse range sophisticated problems but lacked formal criteria for choosing an optimal time step length ( $$\varDelta t$$ ). In Eulerian (grid-based) methods, user can typically reduce arbitrary level expect see corresponding gains in accuracy. The that we consider beha...