Numerical Solutions of Sixth Order Eigenvalue Problems Using Galerkin Weighted Residual Method

Islam, Shafiqul; Farzana, Humaira; Bhowmik, Samir Kumar

doi:10.1007/s12591-016-0323-9

Cited by 5 publications

(6 citation statements)

References 8 publications

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“…The optimal stable, nonnegative Bernstein polynomial basis gained popularity among several researchers and useful properties have been applied to solve regular as well as singular second to higher order BVPs and eigenvalue problems [ [9] , [10] , [11] , 22 , 23 , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] ]. As stated in [22] , the polynomials can be used to form a basis over [0, 1] which is complete.…”

Section: Piecewise Polynomial Basis Functionsmentioning

confidence: 99%

“…Stability and convergence measures [9] for the polynomial estimations in the Galerkin MWR have been studied by several authors [ 9 , 10 , [22] , [23] , [24] , [25] , [31] , [32] , [33] ]. Moreover, orthogonal polynomials basis can approximate general functions in Hilbert spaces.…”

Section: Orthonormal Bernstein-galerkin Techniquementioning

confidence: 99%

“…Lemma: [ 6 , 10 ] : Suppose that the function

times continuously differentiable, i.e.,

, also

be the best approximation

out of

then

, where

…”

Section: Orthonormal Bernstein-galerkin Techniquementioning

confidence: 99%

“…From these discussions, we aim to develop a simple and efficient technique which works well for these kinds of problems with less difficulties. The thermal instability of fluid flow arises in sixth order Benard convection problems and Rayleigh numbers have been studied thoroughly in [ [10] , [11] , [12] ] applying numerous spectral techniques.…”

Section: Introductionmentioning

confidence: 99%

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Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems

2023

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Section: Piecewise Polynomial Basis Functionsmentioning

confidence: 99%

Section: Orthonormal Bernstein-galerkin Techniquementioning

confidence: 99%

“…Lemma: [ 6 , 10 ] : Suppose that the function

times continuously differentiable, i.e.,

, also

be the best approximation

out of

then

, where

…”

Section: Orthonormal Bernstein-galerkin Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems

2023

Self Cite

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“…(3) Solow residual method In 1957, the American economist Solow proposed the method of measuring technological progress-the Solow residual value method. The basic principle is to start from the C-D production function and establish the quantitative relationship between economic growth and various input factors [10]. Assuming that the technological progress is Hicks neutral and grows at a fixed exponential ratio, and then the model is expressed as:…”

Section: Introduction To Specific Theorymentioning

confidence: 99%

Agricultural Human Capital Potential on Agricultural Technology in Western China

2020

AJAS

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Agriculture is the foundation of the national economy, and backward human resources development in the western region is the key factor that causes the gap in human resources between the east and the west. With the resolute battle of poverty alleviation and comprehensive entry into the "zero" stage, it becomes increasingly important to implement precise agricultural technology research in the western region. This research uses literature analysis and qualitative survey methods to investigate and collect basic data on the basis of previous studies. Combined with the practical experience of agricultural enterprise talent development and utilization in Province A, the Solow residual value method is used to return data in Province A Analysis shows that the proportion of junior technical staff is 82%, and the intermediate and senior levels are 12% and 6%, respectively. It is found that the proportion of high-quality agricultural technical staff in Province A is small. Finally, the inductive method is used to summarize the development potential of agricultural human capital and agricultural technology in the western region. This article starts with the basic theories of human resource management, analyzes the current situation and problems of human resource management in western agricultural enterprises, and finds out the shortages and deficiencies that restrict the development and utilization of human resources in western agricultural enterprises. Secondly, through analysis, find out the real needs of agricultural enterprises in the western region regarding talent development and utilization. It is concluded that clarifying the potential of agricultural human capital in the western region and correctly increasing the agricultural human capital in the western region is crucial to the development of agricultural technology in the western region.

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Comparative Study on Sixth Order Boundary Value Problems with Application to Linear Hydrodynamic Stability Problem and Benard Layer Eigenvalue Problem

Farzana

Bhowmik

2019

Differ Equ Dyn Syst

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Numerical Solutions of Sixth Order Eigenvalue Problems Using Galerkin Weighted Residual Method

Cited by 5 publications

References 8 publications

Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems

Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems

Agricultural Human Capital Potential on Agricultural Technology in Western China

Comparative Study on Sixth Order Boundary Value Problems with Application to Linear Hydrodynamic Stability Problem and Benard Layer Eigenvalue Problem

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