Convergence of the directional diffusion splitting method
R. Drebotiy, H. Shynkarenko
TL;DR
This paper proves the convergence of a directional diffusion splitting scheme for solving 2D parabolic and elliptic advection-diffusion-reaction problems under specific conditions on the data.
Contribution
It provides the first rigorous proof of convergence for the directional diffusion splitting method in this context.
Findings
Convergence is established for the scheme under certain restrictions.
The method is applicable to 2D advection-diffusion-reaction problems.
The proof advances theoretical understanding of splitting schemes.
Abstract
We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Advanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics