Numerical Solution of a Nonlinear Fractional Diffusion Problem
DOI:
https://doi.org/10.51699/bvtfbp52Keywords:
: fractional derivative, Caputo derivative, L1 scheme, nonlinear diffusion, semi-implicit schemeAbstract
This article constructs a numerical solution for a nonlinear diffusion equation with a time-fractional derivative. The considered problem is posed on a semi-infinite domain, where the diffusion coefficient is expressed through a power function of the solution. The boundary condition of the problem also has a nonlinear form. The time-fractional derivative is discretized by an L1-type fractional difference approximation, while the spatial operator is discretized by the finite difference method in conservative form. The nonlinear diffusion coefficient is taken from the previous time layer, leading to a semi-implicit scheme. As a result, a tridiagonal system of linear algebraic equations is obtained at each time layer. This approach simplifies the computational process, improves stability, and provides a convenient framework for practical implementation.
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