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

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.