Numerical Analysis of Nonlinear Nonlocal Evolution Problems (NANNEP)

Numerical Analysis of Nonlinear Nonlocal Evolution Problems (NANNEP)
Research Grant MTM2014-54710-P

Departamento de Matemática Aplicada
ETSI Telecomunicación
Universidad de Valladolid
Address
Escuela Técnica Superior de Ingenieros de Telecomunicación
Universidad de Valladolid
Campus Miguel Delibes
Paseo Belén 15
47011 Valladolid
España
Coordenadas GPS
Latitud: N 41.662319
Longitud: W 4.705917

Our research concerns the numerical analysis of three types of nonlocal nonlinear evolution equations that appear in the modelization of applications of interest: (1) Volterra-type equations; (2) Nonlinear nonlocal internal wave equations and (3) nonlinear complex diffusion equations and their application to image restoration. As far as the equations of type (1) are concerned, the proposal will continue to study the numerical analysis of the linear model and will incorporate the construction, implementation and analysis of numerical methods for problems with memory and quasi-linear and nonlinear kernels, emphasizing their application to the restoration of an image. As for the equations of type (2), the proposal is devoted to the design and analysis of pseudospectral and pseudospectral-finite element hybrid methods and their application to the study, by computational means, of the dynamics of solitary waves. The goals of the proposed research for the equations of type (3) are the construction of finite element/volume based discretizations, a study of the scale-space properties of the models and a comparative numerical study of the performance of complex diffusion models for image processing.