Biquaternions for analytic and numerical solution of equations of electrodynamics

TL;DR

This paper reviews recent advances in using biquaternionic techniques to analyze and numerically solve equations in electrodynamics, covering models, integral solutions, and connections to other physical operators.

Contribution

It introduces a biquaternionic framework for electrodynamics equations, including numerical methods and operator relations, enhancing understanding and solution approaches.

Findings

Development of a biquaternionic numerical method for electromagnetic scattering

Integral representations of solutions in electrodynamics

Connections between biquaternionic operators and physical equations

Abstract

We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical method based on biquaternionic fundamental solutions for solving standard electromagnetic scattering problems, relations between different operators of mathematical physics including the Schrodinger, the Maxwell system, the conductivity equation and others leading to a deeper understanding of physics and mathematical properties of the equations.