Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system

Sahu, P. K.; Ray, S. Saha

doi:10.1016/j.amc.2015.01.063

Cited by 52 publications

(32 citation statements)

References 15 publications

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“…There are a lot of studies on application of Haar wavelets in solving differential and integral equations numerically [6,7,9,18,22,24,26,27,29,31,32,40]. Nowadays, Legendre and Chebyshev wavelets are studied by many researchers [3,4,8,13,14,35,36,38,39,[44][45][46][47]. In this paper we propose a Chebyhev wavelet method for solving coupled Burgers' equations numerically.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Oruç¹,

Bulut²,

Esen³

2018

HJMS

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This paper deals with the numerical solutions of one dimensional time dependent coupled Burgers' equation with suitable initial and boundary conditions by using Chebyshev wavelets in collaboration with a collocation method. The proposed method converts coupled Burgers' equations into system of algebraic equations by aid of the Chebyshev wavelets and their integrals which can be solved easily with a solver. Benchmarking of the proposed method with exact solution and other known methods already exist in the literature is made by three test problems. The feasibility of the proposed method is demonstrated by test problems and indicates that the proposed method gives accurate results in short cpu times. Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.

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Section: Introductionmentioning

confidence: 99%

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Oruç¹,

Bulut²,

Esen³

2018

HJMS

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“…Boubaker polynomial [5], Fibonacci collocation method (FCM) [6] and homotopy analysis method (HAM) [7] have been applied to solve Fredholm integro-differential-difference equations with variable coefficients. The system of nonlinear Volterra integro-differential equations has been solved by using Legendre wavelet method [8] and also two dimensional Legendre wavelets have been applied to solve fuzzy integro-differential equations [9]. The integro-differential forms of Lane-Emden equations have been solved by using Legendre multiwavelet method in [10].…”

Section: Introductionmentioning

confidence: 99%

Legendre spectral collocation method for Fredholm integro-differential-difference equation with variable coefficients and mixed conditions

Sahu

Ray

2015

Applied Mathematics and Computation

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“…Wavelet methods have been widely used to obtain numerical solutions of differential equations because of properties such as simplicity, accuracy. Legendre and Chebyshev wavelets studied by many authors [7,16,17,21,18,20,8,19,4,11,12,3] for obtaining numerical solutions of differential and integral equations. In this paper we combine Chebyshev wavelet method with so-called L1 discretization formula to obtain a numerical solution of time fractional Burgers' equation.…”

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confidence: 99%

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation

Oruç¹,

Esen²,

Bulut³

2019

Discrete &Amp; Continuous Dynamical Systems - S

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In this paper, we developed a unified method to solve time fractional Burgers' equation using the Chebyshev wavelet and L1 discretization formula. First we give the preliminary information about Chebyshev wavelet method, then we describe time discretization of the problems under consideration and then we apply Chebyshev wavelets for space discretization. The performance of the method is shown by three test problems and obtained results compared with other results available in literature.

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Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system

Cited by 52 publications

References 15 publications

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

Legendre spectral collocation method for Fredholm integro-differential-difference equation with variable coefficients and mixed conditions

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation

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