Shannon Wavelets for the Solution of Integrodifferential Equations
نویسندگان
چکیده
Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on 1 the Galerking method, 2 the Shannon wavelet representation, 3 the decorrelation of the generalized Shannon sampling theorem, and 4 the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of L2 R functions. Shannon wavelets are C∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series connection coefficients .
منابع مشابه
Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...
متن کاملApplication 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 کاملBernoulli Wavelets Method for Solution of Fractional Differential Equations in a Large Interval
In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...
متن کاملA computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...
متن کاملNUMERICAL SOLUTION OF LINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND BY USING LEGENDRE WAVELETS
In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...
متن کامل