Year: 2026
Type: article
Abstract: Mathematical modeling of heat and mass transfer processes in porous media using fractional derivative equations is of great practical importance. Within the framework of such models, obtaining analytical solutions to the corresponding initial–boundary value problems is generally difficult. In this work, we numerically investigate quasilinear parabolic problems involving Caputo time-fractional derivatives. First, the well-posedness and existence of weak solutions are discussed. Then, we construct and implement a finite-difference scheme that is fourth-order accurate in space and second-order accurate in time. Convergence in the maximum norm is proven. Numerical experiments confirm the accuracy and efficiency of the proposed approach.
Source: Mathematics
DOI: 10.3390/math14040735
Authors: Miglena N. Koleva, Lubin G. Vulkov
Institution: Angel Kanchev University of Ruse
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: European Commission
Award: G1562245063
OpenAlex ID: W7130925276
FWCI:
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