Numerical Solution of Functional Differential Equations using Legendre Wavelet Method
نویسنده
چکیده
In this paper, the objective is to solve the functional differential equations in the following form using Legendre Wavelet Method (LWM), 0 f 0 u(t)=f(t ,u( t) ,u( (t))), t t t u( t)= (t), t t ′ α ≤ ≤ φ ≤ (1) where ƒ: [t0, tƒ]×R→R is a smooth function, α(t) is a continuous function on [t0, tƒ] and φ(t)∈C represents the initial point or the initial data. In the present paper, the most important advantages of using of the proposed method are illustrated. Some experiments are employed to illustrate the validity and flexibility of LWM, in particular for nonlinear functional differential equations.
منابع مشابه
The Legendre Wavelet Method for Solving Singular Integro-differential Equations
In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.
متن کاملConvergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations
In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...
متن کاملNumerical 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 کاملNUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATION BY USING CHEBYSHEV WAVELET OPERATIONAL MATRIX OF INTEGRATION
In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...
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 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