Work

Low-Complexity Numerical Approach for the Diffusion Equation with Variable Diffusion Coefficient

Year: 2026

Type: article

Abstract: The diffusion equation models a wide variety of physical and chemical processes and has significant interest in many scientific disciplines. Analytical and numerical methods found in the literature for solving the diffusion equation consider a constant diffusion coefficient. However, in reality, it is not constant. In this paper, we present a numerical approach to solve the diffusion equation when the diffusion coefficient is not constant. Unlike existing methods that require solving non-linear systems with iterative schemes, our approach transforms the problem into a linear system, drastically reducing computational cost while preserving temporal accuracy.

Source: Mathematics

DOI: 10.3390/math14020285

Authors: Marta Zárraga-Rodríguez, Patricio Fuentes, Xabier Insausti

Institutions: Universidad de Navarra, Naval Research Laboratory Optical Sciences Division

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Eusko Jaurlaritza