37 research outputs found

    Rotation and Magnetic Force Effects on Peristaltic Transport of Non -Newtonian Fluid in a Symmetric Channel

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    In this paper, the impact of magnetic force, rotation, and nonlinear heat radiation on the peristaltic flow of a hybrid bio -nanofluids through a symmetric channel are investigated. Under the assumption of a low Reynolds number and a long wavelength, the exact solution of the expression for stream function, velocity, heat transfer coefficient, induced magnetic field, magnetic force, and temperature are obtained by using the Adomian decomposition method. The findings show that the magnetic force contours improve when the magnitude of the Hartmann number M is high and decreases when rotation increases. Lastly, the effects of essential parameters that appear in the problem are analyzed through a graph. Plotting all figures is done using the MATHEMATICA  software

    New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

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    This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention

    New Challenges Arising in Engineering Problems with Fractional and Integer Order

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    Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem

    Laguerre wavelet solution of Bratu and Duffing equations

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    The aim of this study is to solve the Bratu and Duffing equations by using the Laguerre wavelet method. The solution of these nonlinear equations is approximated by Laguerre wavelets which are defined by well known Laguerre polynomials. One of the advantages of the proposed method is that it does not require the approximation of the nonlinear term like other numerical methods. The application of the method converts the nonlinear differential equation to a system of algebraic equations. The method is tested on four examples and the solutions are compared with the analytical and other numerical solutions and it is observed that the proposed method has a better accuracy.Publisher's Versio

    High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

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    In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the presented methods are efficient and applicable for lower and upper solutions

    Solving Linear Schrödinger Equation through Perturbation Iteration Transform Method

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    This paper applies Perturbation Iteration Transform Method: a combined form of the Perturbation Iteration Algorithm and the Laplace Transform Method to linear Schrödinger equations for approximate-analytical solutions. The results converge rapidly to the exact solution
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