Numerical Solutions of the KdV Equation for Wavelet-Petrov-Galerkin Method - Duarte Vidal, Julio Cesar (2019)
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.