Efficient approximate analytical methods for nonlinear fuzzy boundary value problem

This paper aims to solve the nonlinear two-point fuzzy boundary value problem (TPFBVP) using approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be challenging to evaluate. Therefore, approximate analytical methods may be necessary to consider the solution. Hence, there is a need to formulate new, efficient, more accurate techniques. This is the focus of this study: two approximate analytical methods-homotopy perturbation method (HPM) and the variational iteration method (VIM) is proposed. Fuzzy set theory properties are presented to formulate these methods from crisp domain to fuzzy domain to find approximate solutions of nonlinear TPFBVP. The presented algorithms can express the solution as a convergent series form. A numerical comparison of the mean errors is made between the HPM and VIM. The results show that these methods are reliable and robust. However, the comparison reveals that VIM convergence is quicker and offers a swifter approach over HPM. Hence, VIM is considered a more efficient approach for nonlinear TPFBVPs.

Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids

This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.

Effective task scheduling algorithm in cloud computing with quality of service alert bees and grey wolf optimization

Quality-based services are an indicative factor in providing a meaningful measure. These measures allow labeling for upcoming targets with a numerical comparison with a valid mathematical proof of reading and publications. By obtaining valid designs, organizations put this measure into the flow of technology development operations to generate higher profits. Since the conditions were met from the inception of cloud computing technology, the market was captured heavily by providing support through cloud computing. With the increase in the use of cloud computing, the complexity of data has also increased greatly. Applying natural theory to cloud technology makes it a fruit cream. Natural methods often come true, because survival depends on the live events and happenings, so using it in real life as well as any communication within technology will always be reliable. The numerical results are also showing a better value by comparing the optimization method. Finally, the paper introduces an adaptation theory with effective cloudsim coding of honey bees and grey wolf in conjunction with their natural life cycle for solving task scheduling problems. Using adapted bees improved the results by 50% compared with the original bees and secondly by honeybees and grey wolf improved 60%.

Levenberg-Marquardt method for absolute value equation associated with second-order cone

<p style='text-indent:20px;'>In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.</p>

Structural Imposed Load Analysis of Isotropic Rectangular Plate Carrying a Uniformly Distributed Load Using Refined Shear Plate Theory

This presents the static flexural analysis of a three edge simply supported, one support free (SSFS) rectangular plate under uniformly distributed load using a refined shear deformation plate theory. The shear deformation profile used, is in the form of third order. The governing equations were determined by the method of energy variational calculus, to obtain the deflection and shear deformation along the direction of x and y axis. From the formulated expression, the formulars for determination of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit and its corresponding critical lateral imposed load before plate reaches an elastic yield stress is established. The study showed that the critical lateral imposed load decreased as the plates span increases, the critical lateral imposed load increased as the plate thickness increases, as the specified thickness of the plate increased, the value of critical lateral imposed load increased and increase in the value of the allowable deflection value required for the analysis of the plate reduced the chances of failure of a structural member. This approach overcomes the challenges of the conventional practice in the structural analysis and design which involves checking of deflection and shear after design; the process which is proved unreliable and time consuming. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the depth of the plate variation in predicting the flexural characteristics for an isotropic rectangular SSFS plate. Numerical comparison was conducted to verify and demonstrate the efficiency of the present theory, and they agreed with previous studies. This proved that the present theory is reliable for the analysis of a rectangular plate. Keywords— Allowable deflection, critical imposed load, energy method, plate theories, shear deformation, SSFS rectangular plate

Comparative Study of Various Iterative Numerical Methods for Computation of Approximate Root of the Polynomials

The aim of this article is to present a brief review and a numerical comparison of iterative methods applied to solve the polynomial equations with real coefficients. In this paper, four numerical methods are compared, namely: Horner’s method, Synthetic division with Chebyshev method (Proposed Method), Synthetic division with Modified Newton Raphson method and Birge-Vieta method which will helpful to the readers to understand the importance and usefulness of these methods.

Analytical and numerical comparisons of two methods of estimation of additive × additive × additive interaction of QTL effects

This paper presents the analytical and numerical comparison of two methods of estimation of additive × additive × additive (aaa) interaction of QTL effects. The first method takes into account only the plant phenotype, while in the second we also included genotypic information from molecular marker observation. Analysis was made on 150 doubled haploid (DH) lines of barley derived from cross Steptoe × Morex and 145 DH lines from Harrington × TR306 cross. In total, 153 sets of observation was analyzed. In most cases, aaa interactions were found with an exert effect on QTL. Results also show that with molecular marker observations, obtained estimators had smaller absolute values than phenotypic estimators.

Irregular layout of fiber-optical lines for tomographic monitoring of nautical structures

В статье рассматривается решение волоконно-оптической томографической задачи для мониторинга морских конструкций на основе новой, впервые публично представляемой, схемы укладки волоконно-оптических измерительных линий распределенной сети. В предлагаемой схеме укладки устраняется сдерживающий фактор линейности линий малоракурсной томографии и впервые анализируются возможности неравномерной схемы укладки. Сравнение предложенной схемы укладки с классическими схемами показало преимущество в точности определения места воздействия при уменьшении числа измерительных линий. Численное сравнение полученных результатов вычислительных экспериментов с ранее полученными результатами по другим схемам сканирования показали перспективность предлагаемого способа. Использование неравномерных схем укладок волоконно-оптических линий, наряду с применением систем искусственного интеллекта к информации на выходе этих линий, позволяет их изгибать теоретически на любых поверхностях морских конструкций, огибая углы балок, шпангоутов, неровных уплотнений и других подобных выпуклых поверхностей, для проектирования на их основе систем мониторинга состояния медленных физических полей на поверхностях со сложным произвольным профилем. The article discusses the solution of fiber-optical tomographic problem for monitoring nautical structures based on new layout of fiber-optic measuring lines. In the proposed scheme, the limiting factor of linearity of low-angle tomography lines is eliminated. The possibilities of Irregular layouts are analyzed. Comparison of the proposed layout with classical options showed gain in the accuracy of determining the location of the impact while reducing the number of measuring lines. A numerical comparison of the obtained results of computational experiments with previously obtained results for other scanning schemes showed the promise of the proposed method. Artificial intelligence systems are applied to the output data of these lines. This allows, in theory, to use uneven fiber-optic lines on any surfaces of nautical structures. At the same time, they will be able to bend around the corners of girders, ribs, uneven seals and other similar convex surfaces. All this will make it possible to design on their basis monitoring systems for slow physical fields on random profile surfaces.