Analytical solutions of 1D Maxwell’s equations via infinite-order expansions
Year: 2026
Type: article
Abstract: Analytical solutions to Maxwell’s equations are essential for understanding the causal and instantaneous behavior of electromagnetic fields, yet they are challenging to obtain in open-space settings with general initial values and source terms. This work uses an infinite-order estimation scheme that yields closed-form analytical solutions to Maxwell’s equations. The scheme is expressed as general function-to-function transformations that directly map initial values and source terms to the fields. Several case studies demonstrate the method, producing exact solutions for different initial and source configurations. The results provide both theoretical insight and practical benchmarks for computational electromagnetics.
Source: Results in Applied Mathematics
Author: David Wei Ge
Institution: Microsoft (United States)
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,770
OpenAlex ID: W7128300339