Silviu-Dumitru Pavăl

"Gheorghe Asachi" Technical University of Iasi · Computer Engineering

The paper is concerned with two main topics, as follows. In the first instance, a serious qualitative analysis is performed for a second-order system of coupled PDEs, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as in-homogeneous Neumann boundary conditions. The PDEs system is implementing a SEIRD (Susceptible...

In our current paper we are introducing a new method to enhance semantic image segmentation accuracy of a U-Net neural network model by integrating it with a mathematical model based on reaction-diffusion equations. The methods currently used for semantic image segmentation, including U-Net neural networks, are processing images as blocks of pixels...

In this paper we are addressing two main topics, as follows. First, a rigorous qualitative study is elaborated for a second-order parabolic problem, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain assumptions on the input data: f(t,x), w(t,x) an...

In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of computing its numerical approximation could be of i...

The paper concerns with an implicit first-order in time, finite-differences in space, method to solve numerically a reaction-diffusion equation endowed with a cubic nonlinearity, and non-homogeneous Neumann boundary conditions. Numerical tests for the Allen-Cahn equation are presented and analyzed in terms of the physical quantities of interest.

We present the error analysis of three time-stepping schemes used in the discretization of a nonlinear reaction-diffusion equation with Neumann boundary conditions, relevant in phase transition. We prove L∞ stability by maximum principle arguments, and derive error estimates using energy methods for the implicit Euler, and two implicit-explicit app...

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