Método Wavelet-Galerkin para la solución de Ecuaciones Diferenciales Parciales.
Método Wavelet-Galerkin para la solución de Ecuaciones Diferenciales Parciales. Jairo Villegas Gutiérrez.
Affiliation: Research Group in Functional Analysis and Applications, Mathematical Sciences Department, Universidad EAFIT
Abstract: We describe the use of wavelets for the numerical solution of boundary value problems. We will use wavelets as trial and test functions in a Galerkin approach, the resulting scheme is called the wavelet-Galerkin method. Wavelets have the capability of representing the solutions at different levels of resolutions, which make them particularly useful for developing hierarchical solutions to engineering problems. Accuracy can be improved by increasing either the level of resolution or the order of the wavelet used.
To discretize a PDE problem by Wavelet-Galerkin method, the Galerkin bases are constructed from orthonormal bases of compactly supported wavelets such as Daubechies wavelets. That is, using wavelets allows us to reformuate the differential equation as a discrete infinite-dimensional problem for the unknown wavelet expansion coefficients of the solution.
Escuela de Ciencias Universidad EAFIT. Junio 12 de 2017
Seminario de Doctorado en Ingeniería Matemática Universidad EAFIT
Seminar of the PhD in Mathematical Engineering EAFIT University
Slides: [ pdf ]