On the stability of dual scattering channel schemes

TL;DR

This paper investigates the stability of dual scattering channel schemes, showing that a broad class of alpha-passive processes, including nonlinear cases, are unconditionally stable, extending the known stability of TLM schemes.

Contribution

It demonstrates that many alpha-passive processes ensure unconditional stability in DSC schemes, including nonlinear scenarios, generalizing TLM stability results.

Findings

Alpha-passive processes are unconditionally stable in DSC schemes

Stability results extend to nonlinear situations

Applicable to both TLM and DSC schemes

Abstract

Dual scattering channel (DSC) schemes generalize Johns' TLM algorithm in replacing transmission lines with abstract scattering channels in terms of paired distributions. A well known merit of TLM schemes is unconditional stability, a property that is commonly drawn upon the passivity of linear transmission line networks. So the question arises, if DSC algorithms remain stable in a neat sense. It is shown that a large class of alpha-passive processes are in fact unconditionally stable. The analysis applies to TLM and DSC schemes alike and includes non-linear situations.