Eduardo Cuesta

Convolution quadrature time discretization of fractional diffusion-wave equations

We propose and study a numerical method for time discretization of linear and semilinear integro-partial differential equations that are intermediate between diffusion and wave equations, or are subdiffusive. The method uses convolution quadrature based on the second-order backward differentiation formula. Second-order error bounds of the time discretization and regularity estimates for the solution are shown in a unified way under weak assumptions on the data in a Banach space framework. Numerical experiments illustrate the theoretical results.

A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties

A first order method is considered for the discretization in time of an integro-differential equation, which can be written as

Runge–Kutta convolution quadrature methods for well-posed equations with memory

D^{\alpha} u(t) = A u(t) + f(t)

Cross-Diffusion Systems for Image Processing: II. The Nonlinear Case

,

Generalized fractional integrals in advanced remote sensing

1 < \alpha < 2

Minisymposium: Nonlinear Diffusion Processes: Cross Diffusion, Complex Diffusion and Related Topics

, where

A Discrete Cross-Diffusion Model for Image Restoration

A : D(A) \subset X \to X

On Evolutionary Integral Models for Image Restoration

is a sectorial operator in a Banach space X. Qualitative properties of the numerical solution, such as contractivity and positivity, are studied. A numerical illustration is provided.

Some new learning methodologies on doubt in the framework of Bologna

Runge–Kutta based convolution quadrature methods for abstract, well-posed, linear, and homogeneous Volterra equations, non necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous one is given. The error and stability analysis is based on this representation, which, for the particular case of the backward Euler method, also shows that the numerical solution inherits some interesting qualitative properties, such as positivity, of the exact solution. Numerical illustrations are provided.

A Criticism on the Bologna’s Learning Strategies

In this paper we study the application of