Farzana Humaira, Bhowmik Samir Kumar, Islam Md Shafiqul
Department of Arts & Sciences, Ahsanullah University of Sciences & Technology, Dhaka 1215, Bangladesh.
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.
MethodsX. 2023 Jan 5;10:102006. doi: 10.1016/j.mex.2023.102006. eCollection 2023.
The numerical approximation of eigenvalues of higher even order boundary value problems has sparked a lot of interest in recent years. However, it is always difficult to deal with higher-order BVPs because of the presence of boundary conditions. The objective of this work is to investigate a few higher order eigenvalue (Rayleigh numbers) problems utilizing the method of Galerkin weighted residual (MWR) and the effect of solution due to direct implementation of polynomial bases. The proposed method develops a precise matrix formulation for the eighth order eigenvalue and linear electro-hydrodynamic (EHD) stability problems.•The article explores the same for tenth and twelfth order eigenvalue problems.•This method involves computing numerical eigenvalues using Bernstein polynomials as the basis functions.•The novel weighted residual Galerkin technique's performance is numerically validated by comparing it to other numerical/analytical approaches in the literature.
近年来，高阶偶数阶边值问题特征值的数值逼近引发了诸多关注。然而，由于边界条件的存在，处理高阶边值问题一直颇具难度。本研究的目的是利用伽辽金加权残值法（MWR）研究一些高阶特征值（瑞利数）问题，以及多项式基直接实现对解的影响。所提出的方法为八阶特征值和线性电流体动力学（EHD）稳定性问题建立了精确的矩阵公式。
• 本文对十阶和十二阶特征值问题也进行了同样的探讨。
• 该方法涉及使用伯恩斯坦多项式作为基函数来计算数值特征值。
• 通过与文献中的其他数值/解析方法进行比较，对新型加权残值伽辽金技术的性能进行了数值验证。
