arXiv subjects

Félix del Teso

Publications and source records attributed to Félix del Teso.

38 records · Page 3Linked to original sources

arXiv2013

Finite difference method for a fractional porous medium equation

We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[\frac{\partial u}{\partial t}+(-Δ)^{1/2} (u^m)=0.\] The problem is posed in $x\in \mathbb{R}^N$, $m\geq 1$ and with nonnegative initial data. The fractional Laplacian is implemented via the so-called Caffarelli-Silvestre extension. We prove existence and uniqueness of the solution of this method and also the convergence to the theoretical solution of the equation. We run numerical experiments on typical initial data.

math.AP↗

arXiv2013

Finite difference method for a general fractional porous medium equation

We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[ \frac{\partial u}{\partial t}+(-Δ)^{σ/2} (u^m)=0 \] posed for $x\in \mathbb{R}^N$, $t>0$, with $m\geq 1$, $σ\in (0,2)$, and nonnegative initial data $u(x,0)$. We prove existence and uniqueness of the solution of the numerical method and also the convergence to the theoretical solution of the equation with an order depending on $σ$. We also propose a two points approximation to a $σ$-derivative with order $O(h^{2-σ})$.

math.NA↗