Soluciones Numéricas para la Ecuación KdV Usando el MétodoWavelet-Petrov-Galerkin

• Duarte Vidal, Julio Cesar ^[1] ; Reyes Bahamón, Francisco Javier ^[1]
  1. [1] Universidad Surcolombiana

     Universidad Surcolombiana

     Colombia

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 6, Nº. 2, 2019 (Ejemplar dedicado a: Agosto-Diciembre), págs. 148-155
• Idioma: español
• DOI: 10.17268/sel.mat.2019.02.02
• Títulos paralelos:
  • Numerical Solutions of the KdV Equation for Wavelet-Petrov-Galerkin Method
• Enlaces
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• Resumen
  • español

    Este trabajo Contiene la solución numérica de la ecuación KdV usando el método de Petrov-Galerkin-Wavelet. Lo interesante es poder calcular las integrales Wavelets, usando Wavelets Biortogonales, las propiedades de simetría permiten que los cálculos se reduzcan ostensiblemente. Aquí aplicaremos conceptos del análisis funcional y la teoría de distribuciones inmersos en el cálculo de la derivada débil o derivada distribucional. Hasta obtener gráficamente la solución numérica y la solución analítica de esta ecuación muy usada en la parte de la tecnología deondas y comunicaciones, como también en la reconstrucción de imágenes. Recientemente, los métodos de wavelet se aplican a la solución numérica de ecuaciones diferenciales parciales, trabajos pioneros en esta dirección son las de Beylkin, Dahmen, Jaffard y Glowinski, entre otros.

  • English

    This 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.

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