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This paper conducts an extensive comparative analysis of numerical methods employed in modeling blood flow through arteries with Magnetohydrodynamics (MHD) and hybrid nanofluids. The study investigates the effectiveness and precision of distinct numerical approaches: Akbari Ganji's Method (AGM), Fourth-Order Runge–Kutta (RK4), Finite Volume Method (FVM), and the Finite Element Method (FEM). These methods are essential for comprehending the intricate fluid dynamics that arise in the presence of magnetic fields and hybrid nanofluids a phenomenon relevant in numerous medical applications. Blood flow is subjected to a homogeneous magnetic field in a radial direction while the magneto-hemodynamics effect is taken into account. A variety of medical, physiological, and surgical procedures, as well as the regulation of blood pressure, heat distribution, wound healing, diagnostic imaging, and drug discovery, depend on blood flow through arteries to carry out vital functions such as oxygen and nutrition delivery, organ maintenance, and wound healing. Our findings highlight that while each method has strengths, their applicability varies based on the problem's characteristics and computational resource constraints. This analysis aids researchers and practitioners in selecting the most suitable method for their modeling requirements, advancing numerical techniques for complex fluid dynamics involving MHD and hybrid nanofluids. [ABSTRACT FROM AUTHOR]

This paper introduces a groundbreaking method, Homotopy-based Fourier transform, integrating Fourier transform and Homotopy perturbation for refined nonlinear problem-solving. The modification enhances solution technique efficiency, notably accelerating convergence, particularly in solving the Korteweg–de Vries equation. Demonstrating versatility, the method effectively addresses ordinary and partial differential equations, showcasing its applicability across diverse mathematical scenarios. Moreover, the approach is extended to nonlinear dynamical systems, illustrating its robustness in handling complex dynamic behaviors. This method proves especially suitable for highly nonlinear differential equations, offering an efficient and effective tool for scientists and engineers dealing with intricate mathematical models. By significantly improving convergence rates, the Homotopy-based Fourier transform stands out as a valuable asset in unraveling the complexities of nonlinear systems across various scientific and engineering applications. [ABSTRACT FROM AUTHOR]

Nanofluids with peristaltic flows are being studied in depth because they can be used in so many different ways, such as to diagnose and treat diseases. In this paper, the peristaltic flow of a nanofluid with viscosity and electric conductivity that change with temperature is used. There are different base fluids and nanoparticles that are being thought about. First, the governing equations are modeled, and then they are made easier to understand by assuming that the wavelength is long and the Reynolds number is small. To make a dimensionless differential system, the right dimensionless numbers are added. Mathematica's built-on function NDSolve is used to figure out the numerical solution of the resulting system. To figure out how fast heat moves, researchers compare different combinations of base fluids and nanoparticles. [ABSTRACT FROM AUTHOR]

This paper presents a model of a doubly clamped electrically actuated microbeam, which is a commonly used structure in microelectromechanical systems (MEMS). The model is based on Euler–Bernoulli beam theory and includes the effect of electrostatic forces on the beam's deflection. The electric field is modeled using the parallel plate capacitor model, and the deflection of the beam is calculated using the Galerkin method. The behavior of a microbeam subjected to the van der Waals force, which is a weak intermolecular force that arises from the interaction between the beam and a nearby surface. The microbeam is modeled using the Euler–Bernoulli beam theory, and the van der Waals force is modeled using the Lennard–Jones potential. At the last we study the model of MEMS based on multi-walled carbon nanotubes (MWCNTs). MWCNTs have unique mechanical, thermal, and electrical properties, which make them ideal for use in MEMS applications. The approximate solution of the developed models is found by using homotopy perturbation based Aboodh transformation (HPATM). HPATM is a mathematical method used to solve nonlinear equations by converting them into linear forms. This approach involves introducing a small parameter and applying perturbation theory to obtain a solution in a series form. The method's accuracy is defined based on the existing literature because its solution matched the variation iteration-based Laplace method. Also, we compared its results with the finite difference method. The validity of the stability analysis is further established by examining the stability in the vicinity of the fixed points. Sketches are made of the phase portraits close to the equilibrium points. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for a complex mechanical system consisting of a pendulum with a rolling wheel, which combines translational and rotational motion. The system's dynamics are described by a set of coupled differential equations that are challenging to solve analytically using traditional methods. To overcome this challenge, the variation iteration method (VIM) is employed to derive an analytical solution. VIM is a powerful technique that allows for the approximate solution of differential equations by constructing a series solution iteratively. The Lagrange multiplier, a crucial component in the solution process, is determined for the first time using the Elzaki transformation. Interestingly, the Lagrange multiplier obtained through the Elzaki transformation matches the result obtained from Laplace transformation, which is a fundamental finding of this paper. Also we compared its results with the by employing the VIM and the derived Lagrange multiplier, a comprehensive analytical solution for the complex pendulum with a rolling wheel system is obtained. The solution provides insights into the system's behavior, such as the oscillation amplitudes, angular velocities and other relevant dynamic parameters. The proposed approach demonstrates the efficacy of the VIM in tackling complex mechanical systems and showcases the equivalence between the Lagrange multiplier derived through Elzaki transformation and the well-established Laplace transformation. The results obtained from this study contribute to the understanding and analysis of coupled translational and rotational systems, providing a valuable tool for researchers and engineers working in the field of mechanical dynamics. Sketches are made of the phase portraits close to the equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper, the variational iterative method (VIM) with the Laplace transform is utilized to solve the nonlinear problems of a simple pendulum and mass spring oscillator, which corresponds to the Duffing equation. Finding the Lagrange multiplier (LM) is a significant phase in the VIM, and variational theory is frequently employed for this purpose. This paper demonstrates how the Laplace transform can be utilized to locate the LM in a more efficient manner. The frequency obtained by Laplace-based VIM is the same as that defined in the already existing methods in the literature in order to ensure the clarity of the results. Numerous analytical techniques can be used to solve the Duffing equation, but we are the first to do it using a Laplace-based VIM and a distinctive LM. The fundamental results of my paper are that LM is also the same in the Elzaki transformation. In the vast majority of instances, Laplace-based VIM only requires one iteration to arrive at an answer with high precision and linearization, discretization or intensive computational work is required for this purpose. Comparing analytical results of VIM by Laplace transform to the built-in Simulink command in MATLAB which gives us the surety about the method's applicability for solving nonlinear problems. Future work on the basic pendulum may examine the effects of nonlinearities and damping on its motion and the application of advanced control mechanisms to regulate its behavior. Future research on mass spring oscillators could examine the system's response to random or harmonic input. The mass spring oscillator could also be used in vibration isolation to minimize vibrations from one building to another. [ABSTRACT FROM AUTHOR]

In numerous real-world applications, transverse vibrations of beams are nonlinear in nature. It is a task to solve nonlinear beam systems due to their substantial dependence on the 4 variables of the system and the boundary conditions. To comprehend the nonlinear vibration characteristics, it is essential to do a precise parametric analysis. This research demonstrates an approximation solution for odd and even nonlinear transverse vibrating beams using the Laplace-based variation iteration method, and the formulation of the beams depends on the Galerkin approximation. For the solution of the nonlinear differential equation, this method is efficient as compared to the existing methods in the literature because the solutions exactly match with the numerical solutions. The Laplace-based variation iteration method has been used for the first time to obtain the solution to this important problem. To demonstrate the applicability and precision of the Laplace-based iteration method, several initial conditions are applied to the governing equation for nonlinearly vibrating transverse beams. The natural frequencies and periodic response curves are computed using Laplace-based VIM and compared with the Runge–Kutta RK4 method. In contrast to the RK4, the results demonstrate that the proposed method yields excellent consensus. The Lagrange multiplier is widely regarded as one of the most essential concepts in variational theory. The result obtained are displayed in the table form. Highlights The highlights of the solution of the Euler–Bernoulli beam equation with quintic nonlinearity using Lagrange multiplier are: 1. Introducing the constraint of the boundary conditions into the equation using Lagrange multipliers. 2. Formulating the equations for the Lagrange multipliers and the deflection of the beam. 3. Solving the resulting system of algebraic equations using numerical methods. 4. Obtaining the deflection of the beam as a function of its length and the applied load. 5. Analyzing the behavior of the beam under different loads and boundary conditions. [ABSTRACT FROM AUTHOR]

To find periodic solutions of nonlinear equations, the Jacobi elliptic function expansion method is used. This strategy is more extensive than expanding the hyperbolic tangent series. This approach can produce periodic shock wave solutions such as solitary wave solutions. [ABSTRACT FROM AUTHOR]

For the purpose of constructing the exact periodic solutions of nonlinear wave equations, it has been proposed to use a method known as the Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. It has been demonstrated that the periodic solutions obtained using this method contain both solitary wave solutions and shock wave solutions in some instances. [ABSTRACT FROM AUTHOR]

In this paper, nanoparticles of cobalt oxide (Co3O 4) are prepared at different temperatures 1 2 0 ∘ C, 1 4 0 ∘ C and 1 6 0 ∘ C using the hydrothermal method. Cobalt nitrate hexahydrate: Co (NO 3 ) 2 ⋅ 6 H2O is used as precursor and potassium hydroxide (KOH) is used as precipitating agent. Particle size is controlled using precursor concentration. It is also investigated in this research that particle size increases at high-temperature. Nanoparticles of size between (13.62–17.81 nm) are obtained using this technique (Hydrothermal method). SEM results provide nonuniform distribution of nanoparticles with sharp grain boundaries. Electrical characterization confirms the semiconducting behavior of the material as resistivity decreases with increase in temperature. Electrochemical measurements show detection of hydrogen peroxide H2O2 by nanoparticles of Co3O4. [ABSTRACT FROM AUTHOR]

A computer model of heat transmission in a square cavity was created in order to have a better understanding of the consequences. Temperature differences between the top and bottom walls are what cause convection, whereas the remaining left and right walls remain adiabatic and do not contribute to the process (unheated). In order to provide an accurate estimate of the two-dimensional steady flow inside a square cavity, a novel finite volume (FV) method that incorporates adaptive upwind convection is applied. Due to natural convection's widespread use in the industrial sector, a significant amount of research has been conducted on the topic of how its usage affects the rate of heat transfer in enclosed areas. In a square cavity, the equations for the mass balance, momentum balance, and energy balance of the system are studied. [ABSTRACT FROM AUTHOR]

In this study, we look at the solutions of nonlinear partial differential equations and ordinary differential equations. Scientists and engineers have had a hard time coming up with a way to solve nonlinear differential equations. Almost all of the nature's puzzles have equations that aren't linear. There aren't any well-known ways to solve nonlinear equations, and people have tried to improve methods for a certain type of problems. This doesn't mean, however, that all nonlinear equations can be solved. With this in mind, we'll look at how well the variation approach works for solving nonlinear DEs. Different problems can be solved well by using different methods. We agree that a nonlinear problem might have more than one answer. Factorization, homotropy analysis, homotropy perturbation, tangent hyperbolic function and trial function are all examples of ways to do this. On the other hand, some of these strategies don't cover all of the nonlinear problem-solving methods. In this paper, a new method called the variation iterative method with Laplace transformation is used to find a solution to the highly nonlinear evolution of a simple pendulum whose rotation revolves around its fixed position. When the Laplace operator is used to change the Maximum Minimum Approach, Amplitude Frequency Formulation and Variation Iteration Method (VIM) nonlinear oscillators, the results of the analysis are all the same. The method for solving nonlinear oscillators, as well as their time and boundary conditions, can be shown to be correct by comparing analytical results of VIM obtained through the Laplace transformation. [ABSTRACT FROM AUTHOR]

Quaternion differential equations (QDEs) are a new kind of differential equations which differ from ordinary differential equations. Our aim is to get the exponential matrices for the QDE which is useful for finding the solution of quaternion-valued differential equations, also, we know that linear algebra is very useful to calculate the exponential for a matrix but the solution of QDE is not a linear space. Due to the noncommutativity of the quaternion, the solution set of QDE is a right free module. For this, we must read some basic concepts on Quaternions such as eigenvalues, eigenvectors, Wronskian and the difference between quaternion and complex eigenvalues and eigenvectors; by using the right eigenvalue method for quaternions we developed a fundamental matrix which is useful to construct the exponential matrices which perform a great role in solving the QDEs. [ABSTRACT FROM AUTHOR]