Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution

Mohammadi, Fakhrodin; Hosseini, Mohammad Mehdi; Mohyud‐Din, Syed Tauseef

doi:10.1080/00207721003658194

Cited by 64 publications

(42 citation statements)

References 17 publications

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“…Suppose Ψ(t) be them-dimensional Chebyshev wavelets vector defined in (17), the Itô integral of this vector can be derived as…”

Section: Stochastic Operational Matrix Of Chebyshev Waveletsmentioning

confidence: 99%

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A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations

Mohammadi

2015

IJAMR

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In this paper, the stochastic operational matrix of Itô-integration for the Chebyshev wavelets is applied for solving stochastic Volterra-Fredholm integral equations. The main characteristic of the presented method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Chebyshev wavelets basis is considered. The efficiency and accuracy of the proposed method was demonstrated by some non-trivial examples and comparison with the other existing methods.

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“…Suppose Ψ(t) be them-dimensional Chebyshev wavelets vector defined in (17), the Itô integral of this vector can be derived as…”

Section: Stochastic Operational Matrix Of Chebyshev Waveletsmentioning

confidence: 99%

“…Wavelets permit the accurate representation of a variety of functions and operators [14,15,17,18,19,20,21,16]. In this paper, an stochastic operational matrix for the Chebyshev wavelets is derived.…”

Section: Introductionmentioning

confidence: 99%

A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations

Mohammadi

2015

IJAMR

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“…When the dilation parameter a and the translation parameter b vary continuously, we have the following family of continuous wavelets [10,32,35,36] …”

Section: Second Kind Chebyshev Waveletsmentioning

confidence: 99%

Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

Mohammadi

2017

B Soc Paran Mat

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Stochastic fractional differential equations (SFDEs) have been used for modeling many physical problems in the fields of turbulance, heterogeneous, flows and matrials, viscoelasticity and electromagnetic theory. In this paper, an efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs. In this approach, operational matrices of the second kind Chebyshev wavelets are used for reducing SFDEs to a linear system of algebraic equations that can be solved easily. Convergence and error analysis of the proposed method is considered. Some numerical examples are performed to confirm the applicability and efficiency of the proposed method.

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“…Subrahamanyam et al [17,18,19] applied wavelet collocation method in finite and infinite domains problems arising in engineering. F. Mohammadi et al [7] used Galerkin method with Legendre wavelets to solve this problem with Dirichlet boundary conditions and get good results. In case of Neumann boundary value problems we can not apply a similar procedure as followed in [7].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of two point boundary value problems by wavelet Galerkin method

Upadhyay

Singh

Yadav

et al. 2015

IJAMR

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In this paper, the Legendre wavelet operational matrix of integration is used to solve two point boundary value problems, in which the coefficients of the ordinary differential equation are real valued functions whose inner product with Legendre wavelet basis functions must exist. The method and convergence analysis of the Legendre wavelet is discussed. This method is applied to solve three boundary value and two moving boundary problems. In boundary value problems, we have studied the effects of condition number, elapse time and relative error on Legendre wavelet. It has been observed that the error decreases as the number of wavelet basis function increases. The condition number of square matrix of matrix equation decreases as Legendre wavelet basis function increases. The Legendre wavelet Galerkin method provides better results in lesser time, in comparison of other methods. In case of moving boundary problems the root mean square error (RMSE) for dimensionless temperature, position of moving interface and its generalized time rate are evaluated. It has been observed that the error increases as Stefan number increases.

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Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution

Cited by 64 publications

References 17 publications

A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations

A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations

Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

Numerical solution of two point boundary value problems by wavelet Galerkin method

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