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

Author

Listed:
  • Marta Zárraga-Rodríguez

    (Department of Biomedical Engineering and Sciences, Tecnun-School of Engineering, University of Navarra, 20018 Donostia-San Sebastian, Spain)

  • Patricio Fuentes

    (Photonic Inc., Vancouver, BC V3K 6T1, Canada)

  • Xabier Insausti

    (Department of Biomedical Engineering and Sciences, Tecnun-School of Engineering, University of Navarra, 20018 Donostia-San Sebastian, Spain)

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.

Suggested Citation

  • Marta Zárraga-Rodríguez & Patricio Fuentes & Xabier Insausti, 2026. "Low-Complexity Numerical Approach for the Diffusion Equation with Variable Diffusion Coefficient," Mathematics, MDPI, vol. 14(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:2:p:285-:d:1839360
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