Haar wavelet collocation method for the numerical solution of boundary layer fluid flow problems

Islam, Siraj Ul; Šarler, Božidar; Aziz, Imran; Fazal-i-Haq,

doi:10.1016/j.ijthermalsci.2010.11.017

Cited by 73 publications

(7 citation statements)

References 33 publications

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“…Numerical solution of elliptic boundary value problems with the aid of Haar and Legendre wavelets are discussed by Aziz et al [2]. Numerical solution of boundary layer fluid flow problems was presented by Siraj-ul-Islam et al [15]. Çelik [4] applied the Haar wavelet method for solving magneto-hydrodynamic flow problems.…”

Section: Related Papersmentioning

confidence: 99%

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Lepik

2014

Mathematical Engineering

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Section: Related Papersmentioning

confidence: 99%

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Lepik

2014

Mathematical Engineering

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“…Assume that y ( t ) ∈ L 2 ( R ) with the bounded first derivative on (0,1); then, the error norm at M th level satisfies the following inequality:

where K , C are some real constants [ 28 , 29 ].…”

Section: Convergence Rate Analysismentioning

confidence: 99%

Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs

Pirkhedri

Javadi

Navidi

2014

The Scientific World Journal

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The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed.

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“…We will solve these differential equations by Haar wavelet collocation method (HWCM). Some work using HWCM can be found in the references [20][21][22][23][24][25][26]. In this paper, the fractional derivative (FD) will be considered in the Caputo sense.…”

Section: Introductionmentioning

confidence: 99%

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

2019

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In this paper, a new collocation method based on Haar wavelet is developed for numerical solution of Riccati type differential equations with non-integer order. The fractional derivatives are considered in the Caputo sense. The method is applied to one test problem. The maximum absolute estimated error functions are calculated, and the performance of the process is demonstrated by calculating the maximum absolute estimated error functions for a distinct number of nodal points. The results show that the method is applicable and efficient.

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Haar wavelet collocation method for the numerical solution of boundary layer fluid flow problems

Cited by 73 publications

References 33 publications

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

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