International Journal of Applied and Computational Mathematics

An attempt is made to investigation of MHD natural convection flow of a micropolar fluid due to a permeable moving plate in porous medium in the presence of chemical reaction and radiation. The Lie group analysis used to create similarity transformations and by using those transformations, the system of governing highly non-linear partial differential equations is converted into a set of non-linear coupled ordinary differential equations. The ordinary differential equations thus obtained have been solved by utilizing Keller box method. Numerical solutions for the skin-friction coefficient, Nusselt and Sherwood numbers as well as the velocity, micro-rotation, temperature and concentration are presented graphically for different parametric conditions and discussed in detail. The results show that the skin-friction coefficient reduces with greater values of micro-polar or material parameter and the heat transfer rate advances with reduction in micropolar and radiation parameters. The mass transfer rate accelerates with higher values of chemical reaction parameter.

In this manuscript a chaotic system with exponential term has been considered and studied. Its basic dynamical properties such as time series, phase plots, Lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare section etc. have been discussed and compared with its first, second and third approximate systems. The main aim of this study is to explore the dynamics of the approximations of the exponential chaotic systems. Also, the controllers have been designed to synchronize the chaotic system and its approximations using a technique “compound combination synchronization” and show its application in the field of secure communication. Simulations have been provided to show the efficacy of the used method.

In this paper, second order singularly perturbed convection-diffusion Robin type problem with a discontinuous source term is considered. Due to the discontinuity interior layers appears in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise—uniform mesh for the boundary and interior layers. The method is shown to be parameter uniformly convergent with respect to the singular perturbation parameter. Numerical examples are presented to illustrate the theoretical results.

The main aim of this work is the use of a semi analytical method to obtain series solution of Volterra and Fredholm integral equations of the second kind, the method so-called homotopy asymptotic method. The reliability and consistency of the proposed method is tested by solving different problems and the obtained results are compared with Expansion Iterative Method (EIM), which shows the effectiveness and accuracy of the proposed technique. Moreover, OHAM does not required discretization like other numerical method and also free from small or large parameter assumption. The present technique uses auxiliary function containing auxiliary constants which control the convergence. OHAM is straight forward and easily implementable.

In this present work, the flow of hydromagnetic viscous Walters’ B fluid towards a vertical extending sheet under the consequence of joule heating, chemical reaction, and convective boundary condition is investigated. Initially, the mathematical modeling is constructed, and then the PDEs are changed into the non-linear ODEs with the use of appropriate similarity transformation, and then by using the Optimal-Auxiliary-Functions-Method (OAFM), the system of non-linear ODEs has been solved. By using graphs and tables the behaviors of all the different parameters are described. The graphs show that by increasing Eckart number and Biot number, the temperature profile also increases. On the other hand, by increasing the Soret number, we see that the concentration profile increases, while the opposite impact is shown for higher values of the chemical reaction parameter. The local Sherwood number, Nusselt number, and coefficient of skin friction are identified. Higher thermal buoyancy effect values indicate more serious cooling problems, which are typically encountered in engineering fields and in the manufacturing sector for the cooling of systems or electronic parts. The problem investigated here is important and frequently occurs in a variety of real-world contexts, including the polymerextrusion process. Additionally, it is used in processes such as tinning of copper wires, annealing, drawing, heat-treated materials moving on conveyer belts, manufacture of plastic films, artificial fibers, paper production, crystal growth, and other similar ones.

Linear programming is the optimization of a linear function under constraints of linear equations or inequalities. Since much of the information in the real world is unknown, linear programming does not produce acceptable results due to the need for accurate information and data in many real-world decisions. The grey system is one of the most efficient approaches to dealing with uncertainty and incomplete data. Accordingly, the present study is an attempt to propose a novel method for solving grey linear programming problems. The linear programming with grey information methods presented to date have drawbacks, such as the weakness of solving linear programming with grey information in constraints, inappropriate lower bound results than high bound, a high volume of operations, and high complexity. To address these drawbacks, the present study proposes a novel method of linear programming with grey parameters. As opposed to the other existing methods, which include several steps, the proposed method in this study is much smaller and has only five simple steps. It is easy to work and applicable to any grey linear programming problem.

The thermodynamic study of an unsteady two-dimensional nanofluid flow through a permeable stretched sheet is looked at. Water is used as the primary fluid, along with four different nanoparticles, including copper (Cu), titanium dioxide (TiO2), copper oxide (CuO), and aluminium oxide (Al2O3). The heat transfer phenomenon is explained by an outside source. Additionally considered are the impacts of heat generation and absorption. A similarity transformation is used to convert the considered set of mathematical equations into a system of ODEs. The BVP4C method is then mathematically applied, coupled with shooting fashion. The results are given for cases involving copper nanoparticles. The effects of various physical parameters on the profiles of the dimensionless flow field, temperature, average entropy generation function, skin friction, and the Nusselt number are examined with illustrations and thorough explanations. As exceptional circumstances of the current inquiry, there is a strong agreement between the current conclusion and the findings of the other researchers. The average entropy generation number, temperature, and velocity profiles are shown to be strongly influenced by regulating factors. The authors conclude that the average entropy production number decreased in the existence of a temperature- and space-dependent heat source/sink, but it increased with increasing the viscosity parameter.

Trong tài liệu này, chúng tôi nghiên cứu đồng bộ hóa tổ hợp dự kiến (CPS). Trong CPS, chúng tôi nghiên cứu đồng bộ hóa tổ hợp dự kiến ma trận (MPCS) và đồng bộ hóa tổ hợp dự kiến ma trận ngược (IMPCS) giữa các hệ thống hỗn loạn phức tạp cấp phân không giống nhau khi chịu tác động của độ bất định và sự nhiễu từ bên ngoài. Đồng bộ hóa dự kiến ma trận (MPS) và đồng bộ hóa dự kiến ma trận ngược được đạt được khi hệ số tỷ lệ là một ma trận hằng, điều này đảm bảo độ an toàn cao trong truyền thông an toàn và mã hóa hình ảnh. Dựa trên lý thuyết ổn định Lyapunov và kỹ thuật điều khiển chủ động thích hợp, đồng bộ hóa MPCS và IMPCS giữa hai hệ thống chủ và một hệ thống nô lệ đã được thực hiện. Dựa trên đồng bộ hóa MPCS, chúng tôi trình bày một sơ đồ truyền thông an toàn, trong đó các tín hiệu tin nhắn được truyền qua phương pháp che giấu tín hiệu hỗn loạn. Cuối cùng, các mô phỏng số đã được cung cấp, cho thấy rằng kết quả lý thuyết của chúng tôi hoàn toàn nhất quán với kết quả đồ họa.