Application of Complex Daubechies' Wavelets to Numerical Simulation of a Nonlinear Signal Propagation Model
نویسندگان
چکیده
We report the rst application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the electric eld amplitude in nonlinear optical bers. We propose and study a new way to implement a global space-time adaptive grid, based on interpolation properties of higher-order scaling functions.
منابع مشابه
Application of Daubechies wavelets for solving Kuramoto-Sivashinsky type equations
We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition. Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method. The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method.
متن کاملA wavelet method for stochastic Volterra integral equations and its application to general stock model
In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...
متن کاملA new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells
This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...
متن کاملThe collocation method for Hammerstein equations by Daubechies wavelets
The numerical solutions to the nonlinear integral equations of Hammerstein-type y(t) =f(t) + 11 k(t,s)g(s,y(s))ds, t E [0,1] with using Daubechies wavelets are investigated. A general kernel scheme basing on Daubechies wavelets combined with a collocation method is presented. The approach of creating Daubechies interval wavelets and their main properties are briefly mentioned. Also we present a...
متن کاملSimulation of the Mode I fracture of concrete beam with cohesive models
Crack propagation modeling in quasi-brittle materials such as concrete is essential for improving the reliability and load-bearing capacity assessment. Crack propagation explains many failure characteristics of concrete structures using the fracture mechanics approach. This approach could better explain the softening behavior of concrete structures. A great effort has been made in developing nu...
متن کامل