Analysis of general unified MHD boundary-layer flow of a viscous fluid - a novel numerical approach through wavelets

Karkera, Harinakshi; Katagi, Nagaraj N.; Kudenatti, Ramesh B.

doi:10.1016/j.matcom.2019.08.004

Cited by 30 publications

(19 citation statements)

References 43 publications

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“…By applying the method of FDCHPs pseudo-Galerkin, with shifting the given interval to [−1, 1], we obtain 9.39 × 10 −18 after four iterations as a MAE. On the other hand, the method in [50] obtained a MAE of almost 10 −06 after 2 9+1 = 1024 iterations.…”

Section: Resultsmentioning

confidence: 97%

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Abdelhakem

Alaa-Eldeen²,

Băleanu

et al. 2021

Fractal Fract

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An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis of functions, consisting of first derivatives of Chebyshev polynomials, has been used. Consequently, new operational matrices for derivatives of any integer order have been introduced. An error analysis is performed to ensure the convergence of the presented method. In addition, the accuracy and the efficiency are verified by solving BVPs examples, including real-life problems.

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Section: Resultsmentioning

confidence: 97%

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Abdelhakem

Alaa-Eldeen²,

Băleanu

et al. 2021

Fractal Fract

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“…Also, many applications are described by higher-order BVPs as in Magnetohydrodynamic flow (Karkeraa et al. 2020 ) and transverse vibration of a uniform beam (Khalil et al. 2012 ; El-Kady et al.…”

Section: Introductionmentioning

confidence: 99%

Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

et al. 2022

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We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices’ efficiency and accuracy.

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“…Unfortunately, these ordinary differential equations (ODEs) often have no analytical solutions. Consequently, the focus on the approximate solutions of them has grown 3,4 . Many researchers introduced and developed novel methods for solving these kinds of problems; see, for example, previous studies 5–7 .…”

Section: Introductionmentioning

confidence: 99%

A robust spectral treatment of a class of initial value problems using modified Chebyshev polynomials

Youssri

Abd-Elhameed

Abdelhakem

2021

Math Methods in App Sciences

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New modified shifted Chebyshev polynomials (MSCPs) have been constructed over the interval [α, β]. These polynomials are utilized as basis functions with the application of the spectral collocation method. The operational matrix of integer order derivatives of these polynomials is introduced. The elements of this matrix are explicitly given. The introduced operational matrix along with the collocation method is used to find a direct solver of linear/nonlinear class of IVPs. Furthermore, the convergence and error analysis of the modified Chebyshev expansion are discussed. Some specific numerical examples are given to ascertain the wide applicability and the good efficiency of the suggested algorithm. The obtained results from the tested numerical examples are convincing. Also, the introduced approximate solutions are very close to the analytical ones.

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Analysis of general unified MHD boundary-layer flow of a viscous fluid - a novel numerical approach through wavelets

Cited by 30 publications

References 43 publications

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

A robust spectral treatment of a class of initial value problems using modified Chebyshev polynomials

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