1. Soluciones Numéricas para la Ecuación KdV Usando el MétodoWavelet-Petrov-Galerkin
- Author
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Francisco Javier Reyes and Julio Cesar Duarte
- Subjects
Physics ,ecuación kdv ,wavelets biortogonales ,lcsh:T57-57.97 ,lcsh:Mathematics ,lcsh:Applied mathematics. Quantitative methods ,Applied mathematics ,método de petrov-galerkin ,ecuación diferencial parcial ,integrales wavelets ,Korteweg–de Vries equation ,lcsh:QA1-939 - Abstract
espanolEste trabajo Contiene la solucion numerica de la ecuacion KdV usando el metodo de Petrov-Galerkin-Wavelet. Lo interesante es poder calcular las integrales Wavelets, usando Wavelets Biortogonales, las propiedades de simetria permiten que los calculos se reduzcan ostensiblemente. Aqui aplicaremos conceptos del analisis funcional y la teoria de distribuciones inmersos en el calculo de la derivada debil o derivada distribucional. Hasta obtener graficamente la solucion numerica y la solucion analitica de esta ecuacion muy usada en la parte de la tecnologia deondas y comunicaciones, como tambien en la reconstruccion de imagenes. Recientemente, los metodos de wavelet se aplican a la solucion numerica de ecuaciones diferenciales parciales, trabajos pioneros en esta direccion son las de Beylkin, Dahmen, Jaffard y Glowinski, entre otros. EnglishThis work contains the numerical solution of the KdV equation using the Petrov-Galerkin-Wavelet method. The interesting thing is to be able to calculate Wavelet integrals, using Biorthogonal Wavelets, the properties of symmetry allow the calculations to be significantly reduced. Here we will apply concepts of functional analysis and the theory of distributions immersed in the calculation of the weak derivative or distributional derivative. To obtain graphically the numerical solution and the analytical solution of this equation very used in the part of the wave and communications technology, as well as in the reconstruction of images. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneering works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others.
- Published
- 2019