Collocation method applied to unsteady flow of gas through a porous medium

Upadhyay, Subrahamanyam; Rai, K.N.

doi:10.14419/ijamr.v3i3.2924

Cited by 9 publications

(6 citation statements)

References 14 publications

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“…a set of CSRBFs with these properties were proposed for providing an effective but simple way to improve the convergence rate. A comparison was made among the solutions of [14,17] and this work. the absolute error Res 2 were obtained.…”

Section: Resultsmentioning

confidence: 99%

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Application of Meshfree Method Based on Compactly Supported Radial Basis Function for Solving Unsteady Isothermal Gas Through a Micro–Nano Porous Medium

Parand

2017

Iran J Sci Technol Trans Sci

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In this paper, we have applied the Meshless method based compactly supported radial basis function collocation for obtaining the numerical solution of unsteady gas equation. The unsteady gas equation is a second order non-linear two-point boundary value ordinary differential equation on the semi-infinite domain, with a boundary condition in the infinite. The compactly supported radial basis function collocation method reduces the solution of the equation to the solution of a system of algebraic equation. also, we compare the results of this work with some results. It is found that our results agree well with those by the numerical method, which verifies the validity of the present work.

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Section: Resultsmentioning

confidence: 99%

“…he applied the modified Laplace decomposition method (MLDM) coupled with Padé approximation to compute a series solution of unsteady flow of gas through a porous medium. Upadhyay and Rai [17] using the Legendre wavelet collocation method (yL-WCM) to solve this equation.…”

Section: Unsteady Gas Problemmentioning

confidence: 99%

Application of Meshfree Method Based on Compactly Supported Radial Basis Function for Solving Unsteady Isothermal Gas Through a Micro–Nano Porous Medium

Parand

2017

Iran J Sci Technol Trans Sci

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“…This method applied central finite element formulae in the boundary value problems of partial differential equations to convert them into initial value problems of a system of matrix of ordinary differential equations, and the Chebyshev polynomial Galerkin method is applied in the initial value problem to transfer into a system of algebraic equations. Recently, Yadav et al and Upadhyay and Rai applied Legendre wavelet–based Galerkin, Spectral Galerkin and collocation methods in boundary value and moving boundary problems and found excellent results. Yadav et al presented an analytical finite element Legendre wavelet Galerkin solution of the free‐boundary problem of heat conduction.…”

Section: Introductionmentioning

confidence: 99%

“…are taken for odd and even points. The formulas(29) to(32) are the generalization of fourth point's formula for the initial slope.…”

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confidence: 99%

Finite difference Legendre wavelet collocation method applied to the study of heat mass transfer during food drying

Upadhyay

Singh

Rai

2019

Heat Trans. Asian Res.

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In this paper, we studied a single‐phase‐lag model of heat and moisture transfer in a finite slab, cylinder or sphere, undergoing industrial drying of foods. The present model is a boundary value problem of a system of two nonlinear second‐order hyperbolic partial differential equations. The solution of the present is model obtained by using finite difference Legendre wavelet collocation (FDLWCM) and Galerkin methods. In case of constant moisture diffusivity, we observe that the finite difference Legendre wavelet Galerkin and collocation solutions are exactly the same. Laplace transform and FDLWCM solutions are approximately the same. The L 2 norm error decreases as Legendre wavelet basis functions increases and strip size decreases. The L 2 norm relative error increases as Luikov number increases. L 2 norm relative error is highest in cylindrical shape and lowest in slab shape while in between spherical shape. The effects of the dimensionless parameters of heat and mass transfer are discussed in detail.

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“…As described before, spectral (Galerkin, Tau and Pseudo-spectral) methods do not work well for this kind of problem. 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.…”

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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Collocation method applied to unsteady flow of gas through a porous medium

Cited by 9 publications

References 14 publications

Application of Meshfree Method Based on Compactly Supported Radial Basis Function for Solving Unsteady Isothermal Gas Through a Micro–Nano Porous Medium

Application of Meshfree Method Based on Compactly Supported Radial Basis Function for Solving Unsteady Isothermal Gas Through a Micro–Nano Porous Medium

Finite difference Legendre wavelet collocation method applied to the study of heat mass transfer during food drying

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

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