On the Approximation of a Continuous Function f(x, y) by its Two Dimensional Legendre Wavelet Expansion
نویسندگان
چکیده
1. Natanson I. P.(1949), Constructive Function Theory, Gosudarstvennoe Izdatel’stvo Tehniko-Teoreticeskoi Literatury, Moscow . 2. Chui C. K.(1992), An Introduction to wavelets(Wavelet analysis and its applications), Vol. 1, Academic Press, USA. 3. Daubechies I.(1992) ,”Ten Lectures on Wavelets” SIAM, Philadelphia. 4. Meyer Y.(1993), (Toulouse (1992))(Meyer Y. and Roques S.,eds.), Frontiers, vette Gif-sur-Y, Wavelets their post and their future, Progress in Wavelet analysis applications, pp.9-18.
منابع مشابه
Numerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method
In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...
متن کاملModified Wavelet Method for Solving Two-dimensional Coupled System of Evolution Equations
As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...
متن کاملAPPROXIMATION SOLUTION OF TWO-DIMENSIONAL LINEAR STOCHASTIC FREDHOLM INTEGRAL EQUATION BY APPLYING THE HAAR WAVELET
In this paper, we introduce an efficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.
متن کاملRecurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials
Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$ x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x),$$ we find the coefficients $b_{i,j}^{(p,q,ell ,,r)}$ in the expansion $$ x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell }y^{r}f^{(p,q)}(x,y) =sumli...
متن کاملA numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximation
The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential techniq...
متن کامل