On quasi-linear PDAEs with convection: applications, indices, numerical solution

TL;DR

This paper investigates quasi-linear partial differential algebraic equations with convection, focusing on index determination, numerical solutions via finite difference splitting, and an application to plasma physics.

Contribution

It introduces a method to determine the index of quasi-linear PDAEs with convection and develops a modified fractional step numerical scheme for their solution.

Findings

Convergence of the numerical scheme towards the exact solution is demonstrated.

Application to plasma physics showcases the method's practical relevance.

Numerical results validate the effectiveness of the proposed approach.

Abstract

For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an application from plasma physics. Especially we discuss the numerical solution of initial boundary value problems by means of a corresponding finite difference splitting procedure which is a modification of a well known fractional step method coupled with a matrix factorization. The convergence of the numerical solution towards the exact solution of the corresponding initial boundary value problem is investigated. Some results of a numerical solution of the plasma PDAE are given.