In this paper, the Elzaki transform decomposition method is implemented to solve the time-fractional Swift–Hohenberg equations. The presented model is related to the temperature and thermal ...convection of fluid dynamics, which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In the Caputo manner, the fractional derivative is described. The suggested method is easy to implement and needs a small number of calculations. The validity of the presented method is confirmed from the numerical examples. Illustrative figures are used to derive and verify the supporting analytical schemes for fractional-order of the proposed problems. It has been confirmed that the proposed method can be easily extended for the solution of other linear and non-linear fractional-order partial differential equations.
This paper presents a computational model using Quartic Trigonometric Tension B-spline (QT-TB) function with collocation approach for nonlinear dispersive wave equation. Shallow water wave modeling ...plays a crucial role in various fields, including coastal engineering, oceanography, and natural hazard assessment. The QT-TB function is employed for spatial derivatives, integrating the nonlinear term through the linearization technique. While maintaining most characteristics of traditional polynomial B-splines, this method improves numerical solutions, enhancing accuracy in modeling. The performance of the method is rigorously assessed across three benchmark problems, with results compared to those of prior studies employing identical parameters. Detailed numerical illustrations are presented. Graphical representations are utilized to illustrate the single solitary wave motion, dynamics of coupled solitary waves and dynamics of triplet solitary waves in this study. Numerical experiments validate the method's accuracy and efficiency in capturing RLW-driven wave dynamics, establishing it as a reliable tool for various applications. The presented work includes an analysis of the stability of the proposed scheme, employing the Fourier method and shows that its unconditional stable.
The present investigation dealing with a hybrid technique coupled with a new iterative transform method, namely the iterative Elzaki transform method (IETM), is employed to solve the nonlinear ...fractional Fisher’s model. Fisher’s equation is a precise mathematical result that arose in population dynamics and genetics, specifically in chemistry. The Caputo and Antagana-Baleanu fractional derivatives in the Caputo sense are used to test the intricacies of this mechanism numerically. In order to examine the approximate findings of fractional-order Fisher’s type equations, the IETM solutions are obtained in series representation. Moreover, the stability of the approach was demonstrated using fixed point theory. Several illustrative cases are described that strongly agree with the precise solutions. Moreover, tables and graphs are included in order to conceptualize the influence of the fractional order and on the previous findings. The projected technique illustrates that only a few terms are sufficient for finding an approximate outcome, which is computationally appealing and accurate to analyze. Additionally, the offered procedure is highly robust, explicit, and viable for nonlinear fractional PDEs, but it could be generalized to other complex physical phenomena.
We put into practice relatively new analytical techniques, the Shehu decomposition method and the Shehu iterative transform method, for solving the nonlinear fractional coupled Korteweg-de Vries ...(KdV) equation. The KdV equation has been developed to represent a broad spectrum of physics behaviors of the evolution and association of nonlinear waves. Approximate-analytical solutions are presented in the form of a series with simple and straightforward components, and some aspects show an appropriate dependence on the values of the fractional-order derivatives that are, in a certain sense, symmetric. The fractional derivative is proposed in the Caputo sense. The uniqueness and convergence analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. It is worth mentioning that the proposed methods are powerful and are some of the best procedures to tackle nonlinear fractional PDEs.
With the presence of the odd viscosity, the linear instability of a planar jet (sheet) surrounded by an inviscid gas medium is explored for varicose and sinuous modes. The previous studies on sheet ...mechanics did not consider the role of the odd viscosity when measuring the maximum growth rate, dominant wave number, instability limit, and breakup length. Semi-dominant characteristic of the odd viscosity is that it is a stabilizing factor for the state of a liquid sheet. It is an unstable factor in a few cases as dictated by the model parameters, such as the odd viscosity number, aerodynamic force, Reynolds number, ambient gas density, and Weber number. In the production of metal alloys, metal powders, and the cooling and descaling stages of downstream metal manufacturing processes, particularly in the steel industry, sprays may be employed in a variety of ways.
Background. A large proportion of elderly people suffer from hypovitaminosis D, and depending on the severity of the condition, they develop complications that are detrimental to their health. ...Objective. To determine the consistency between the results of the vitamin D level in the blood compared to the result with the score of a simple questionnaire (Physician Vitamin D Status Predictor - VDSP) for elderly patients. Subjects and methods. This is a cross-sectional study conducted during the period between October 2018 and November 2019 in 3 primary health care centres (PHCCs) in Jeddah, Saudi Arabia. The subjects for this study were patients aged 60 or older. Data were collected in two phases: a questionnaire approach as the first phase, while the second phase involved blood testing for vitamin D levels. The validated questionnaire used in this study was the Physician`s Vitamin D Status Predictor (VDSP). Results. The study included 335 participants who ranged between 60 and 107 years old with a mean age of 68.2 years and standard deviation (SD) of 7.3 years. Females represented 66.9% of the total participants. The prevalence of vitamin D deficiency was 60.8%; among them, 7.2% were categorized as severe deficiency, whereas the prevalence of vitamin D insufficiency was 29.9%. The outcomes of VDSP survey were not directly associated with serum 25(OH)D levels in elderly people, except for the number of medications. In addition, vitamin D supplementation was associated with serum 25(OH)D levels among those patients. Conclusion. Vitamin D supplementation was significantly associated with serum 25(OH)D levels. Moreover, this study showed a significant association between serum 25(OH)D levels and the number of medications taken by the participants.
Enhancement of heat transfer due to stretching sheets can be appropriately controlled by the movement of the nanofluids. The concentration and settling of the nanoparticles in the viscous MHD fluid ...and bioconvection are addressed. In this scenario, the fluid flow occurring in the presence of a normal and uniform magnetic field, thermal radiation, and chemical reaction is taken into account. For the two-dimensional flow with heat and mass transfer, five dependent variables and three independent variables constitute the system of partial differential equations. For this purpose, similarity functions are involved to convert these equations to corresponding ODEs. Then, the Runge–Kutta method with shooting technique is used to evaluate the required findings with the utilization of MATLAB script. The fluid velocity becomes slow against the strength of the magnetic parameter. The temperature rises with the parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruences.
This article aims to produce efficient numerical results using the Galerkin approach and quartic B-spline functions for the one-dimensional second-order nonlinear evolution equation. The quartic ...B-spline functions are used as the shape and weight functions for the Galerkin method. The time derivative and space parameters are discretized by the finite difference and Crank-Nicolson schemes, respectively. A Galerkin approach is investigated by propagating waves at various times and comparisons are made with published papers. The obtained results show that the scheme presented good results and conservations laws are all adequately obeyed.
Peristalsis has recently been a hot topic in biomedical engineering and biological sciences because of its importance. This paper provides a rudimentary insight into the peristaltic transport of an ...MHD fractional fluid over a permeable medium in a non-uniform channel that is the aim of the research. In mathematical modeling, fluid fills the porous region according to an altered Darcy's law. The derived equations were solved analytically via the long-wavelength hypothesis reliant on the small Reynolds number hypothesis, to solve the leading equations. Temperature, velocity, pressure gradient, friction forces, and pressure rise are all solved using confined solutions. The obtained results were validated with the state-of-threat literature reports. It was claimed that our systematic approach. The numerical results are computed, discussed numerically, and graphs are used to present them. The effects of relevant parameters on the previously mentioned quantities are investigated by plotting graphs based on the computational results. The results show that the parameter effect is extremely powerful. As a limiting case of the problem considered, an adequate comparison with prior results in the literature has been made.
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