The Finite difference method for the Minkowski Curve
Nizare Riane, Claire David
TL;DR
This paper introduces a finite difference approach to approximate solutions of partial differential equations on the Minkowski self-similar curve, expanding numerical methods to fractal geometries.
Contribution
It presents a novel finite difference method tailored for PDEs on Minkowski fractal curves, a previously unexplored geometric setting.
Findings
Successful approximation of PDE solutions on Minkowski curves
Extension of finite difference methods to fractal geometries
Potential for broader applications in complex geometric domains
Abstract
In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods