Numerical solution of the convection diffusion equations by the second kind Chebyshev wavelets

Zhou, Fengying; Xu, Xiaoyong

doi:10.1016/j.amc.2014.08.091

Cited by 38 publications

(40 citation statements)

References 15 publications

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“…The results for example 1 are displayed in Table I. For the purpose of comparison in Table I, we compare the absolute error of our method with different values of J with the method in [20]. The space-time diagram of the exact and approximate solutions are shown in Fig.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Ashpazzadeh

Lakestani

2018

bspm

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A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diffusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diffusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.Key Words: Hermite interpolant multiscaling functions, Convection-diffusion equation, operational matrix of derivative, Operational matrix of integration, operational matrix of product.

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Section: Numerical Experimentsmentioning

confidence: 99%

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Ashpazzadeh

Lakestani

2018

bspm

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“…Recently, in [19], the authors gave a new class of fractional variational problems and solved this using a decomposition formula based on Jacobi polynomials. The operational matrix methods (see [35][36][37][38][39][40][41]) have been found to be useful for solving problems in fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials

Singh¹,

Pandey

Srivástava

2019

Mathematics

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The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method. The Ritz method has allowed many researchers to solve different forms of fractional variational problems in recent years. The NLFVP is solved by applying the Ritz method using different orthogonal polynomials. Further, the approximate solution is obtained by solving a system of nonlinear algebraic equations. Error and convergence analysis of the discussed method is also provided. Numerical simulations are performed on illustrative examples to test the accuracy and applicability of the method. For comparison purposes, different polynomials such as 1) Shifted Legendre polynomials, 2) Shifted Chebyshev polynomials of the first kind, 3) Shifted Chebyshev polynomials of the third kind, 4) Shifted Chebyshev polynomials of the fourth kind, and 5) Gegenbauer polynomials are considered to perform the numerical investigations in the test examples. Further, the obtained results are presented in the form of tables and figures. The numerical results are also compared with some known methods from the literature.

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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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Numerical solution of the convection diffusion equations by the second kind Chebyshev wavelets

Cited by 38 publications

References 15 publications

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

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