The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some specific cases of time-dependent diffusion equations. Moreover, the maximum absolute error () is determined to demonstrate the accuracy of the proposed techniques.
Polyacrylonitrile nanofiber (PANFS), a well-known polymers, has been extensively employed in the manufacturing of carbon nanofibers (CNFS), which have recently gained substantial attention due to their excellent features, such as spinnability, environmental friendliness, and commercial feasibility. Because of their high carbon yield and versatility in tailoring the final CNFS structure, In addition to the simple formation of ladder structures through nitrile polymerization to yield stable products, CNFS and PAN have been the focus of extensive research as potential production precursors. For instance, the development of biomedical and high-performance composites has now become achievable. PAN homopolymer or PAN-based precursor copolymer can
... Show MoreNatural frequency under initial stresses for simply supported cross-ply composite laminated plates (E glass- fiber) are obtained using Refind theory (RPT). This theory accounts for parabolic distribution of the transverse shear strain through the plate thickness and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. The governing equations for Eigen value problem under initial stress are derived using Hamilton’s principle and solved using Navier solution for simply supported cross-ply symmetric and antisymmetric laminated plates. The effect of many design factors such as modulus ratio, thickness ratio and number of laminates on the Natural frequency and buckling stresses
... Show MoreThis paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.
In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.
Wireless sensor networks (WSNs) represent one of the key technologies in internet of things (IoTs) networks. Since WSNs have finite energy sources, there is ongoing research work to develop new strategies for minimizing power consumption or enhancing traditional techniques. In this paper, a novel Gaussian mixture models (GMMs) algorithm is proposed for mobile wireless sensor networks (MWSNs) for energy saving. Performance evaluation of the clustering process with the GMM algorithm shows a remarkable energy saving in the network of up to 92%. In addition, a comparison with another clustering strategy that uses the K-means algorithm has been made, and the developed method has outperformed K-means with superior performance, saving ener
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