# Characteristics-based Simulink implementation of first-order quasilinear partial differential equations

## TL;DR

This paper presents a characteristics-based Simulink subsystem for solving first-order quasilinear PDEs, offering improved numerical stability and accuracy over traditional space discretization methods, demonstrated through a feedback example.

## Contribution

It introduces a novel Simulink implementation of the method of characteristics for PDEs, enhancing stability and accuracy in online simulation environments.

## Key findings

- Better numerical stability than space discretization methods
- Achieved higher accuracy in a feedback control example
- Implementation is publicly available for diverse models

## Abstract

The paper deals with solving first-order quasilinear partial differential equations in an online simulation environment, such as Simulink, utilizing the well-known and well-recommended method of characteristics. Compared to the commonly applied space discretization methods on static grids, the characteristics-based approach provides better numerical stability. Simulink subsystem implementing the method of characteristics is developed. It employs Simulink's built-in solver and its zero-crossing detection algorithm to perform simultaneous integration of a pool of characteristics as well as to create new characteristics dynamically and discard the old ones. Numerical accuracy of the solution thus obtained is established. The subsystem has been tested on a full-state feedback example and produced better results than the space discretization-based "method of lines". The implementation is available for download and can be used in a wide range of models.