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Acoustic fluid solid interaction (AFSI) has been a subject of high interest for the last decade and the literature is now extensive. Noise transmission into and radiation from a rectangular cavity through a flexible structure in a noisy/thermal environment at supersonic flow is studied. In the present book, the pre/post -flutter regions are considered in a nonlinear study. The governing equations of flexible panel are constructed using Von Karman theory, first-order piston theory and a modal cavity formulation, also a stationary homogeneous turbulent-boundary-layer (TBL) is modeled based on experimental data through stochastic modeling. The thermal environment and external incident random noise are also considered and the far-field sound is predicted with a boundary integral method. The Rayleigh-Ritz approach is adopted to discretize the partial differential equations of the AFSI system, and the resulting ordinary differential equations (ODEs) are solved numerically by the fourth-order Runge-Kutta with Matlab. additionally, Matlab codes are presented in the Appendix section.

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The Numerical analysis is taught in undergraduate mathematics, physics, engineering and post graduate physics classes. The solution of differential equation is basic need in these courses, where the numerical method is the main tool to solve ordinary and partial differential equations, described in the textbook with fully-worked examples followed by the concerned theory and schematic representation of algorithm. The text is divided into four topics: The Solution of 1st order ODE,Solution of 2nd order ODE,Linear Boundary value problem and the Solution of PDE. The topics includes eleven methods: The Euler & Modified Euler, Runge-Kutta, Predictor-Corrector, Numerov, Taylor, Finite difference, Linear Shooting, Gauss Elimination, Gauss Jordan, Gauss seidal & SOR, Forward & Central difference and the Crank Nicholson. The methods are followed by applied examples, Computational Formulae and Objective & Subjective Exercises. The work is greatly useful to the under graduate students of maths, science and engineering moreover it is a good reference material for the teachers to conduct course covering numerical methods in concerned disciplines.

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The fluid flow due to a stretching cylinder encounters in several industrial manufacturing processes. Such processes are fiber technology, drawing of plastic films, paper production, extrusion processes and of theoretical interest etc. Present study deals with the numerical solutions for mass transfer flow problems of Newtonian and Non-Newtonian fluids. The effect of mass transfer on axisymmetric laminar boundary layer flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is investigated. The boundary layer equations in cylindrical form are first transformed into a set of non-dimensional ordinary differential equations using dimensionless variables and then solved by Runge-Kutta method with Shooting Technique. The problem under consideration reduces to the flat plate case so that the curvature parameter is absent, and thus the results obtained can be examined.

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This book deals with the elementary aspects of flow, heat and mass transfer of boundary layer flow problems related to magneto hydrodynamic non- Newtonian nanofluid flows , with special emphasis on slip flow and melting heat transfer so that the subject is perceived by the post graduate students, researchers and post-doctoral researchers. This text also introduces numerical computational tools for solving differential equation models that arise in fluid flow, heat and mass- transfer of non-Newtonian fluids. This study is essentially numerical in character. By applying the similarity transformations, the system of non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations. Obtained equations are then solved numerically using Runge-Kutta-Fehlberg-45 order method along with Shooting technique.

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In this work, similarity and numerical solutions for some problems of unsteady heat transfer over different surfaces in the boundary layer of fluids through a porous medium are discussed. In these problems, we studied the influences of magnetic field, permeability of porous medium, heat generation / absorption, thermal conductivity, variable temperature. The governing equations are first cast into a dimensionless form by a nonsimilar transformation and the resulting equations are solved numerically by using the Runge-Kutta numerical integration, procedure in conjunction with shooting technique. The obtained results are shown in graphics and tabulated representation followed by a quantitative discussion. The main aim of this book which consists of four chapters, is to study similarity solutions of boundary layer of some fluid. In the following, a brief discussion of the chapters is given.

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This introductory text teaches foundational concepts in numerical mathematics. It uses real-world examples, representational graphs, solved tutorials, practice problems, flow diagrams, algorithms and computer programs to enrich knowledge and strengthen understanding. It covers contemporary numerical method techniques, such as root finding methods, difference calculus and interpolation principle. It explains existing traditional techniques used in solving engineering and process-based tasks involving numerical differentiation and integration, such as Euler's method, rectangular method, trapezium method and the Runge-Kutta family of methods. It discusses initial value problems, uniform partition, non-uniform partition, Cauchy equation, Lagrange interpolation and boundary value problems. Finally, it also covers root finding methods including fixed-point, bisection, regula- falsi, Secant and Newton methods. The book is ideal as a one-semester text on numerical methods and its related disciplines. It is also relevant to other readers as a reference manual.

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The purpose of this work is to determinate the approximate solutions of boundary value problems with conditions inside the interval (0,1) using collocation method with global B-splines functions of degree k(order k+1), orthogonal polynomials Chebyshev and combined methods with B-splines functions or C.C method and Runge-Kutta methods. We do a comparative study of these numerical methods, making their implementation of algorithms written in MATLAB 2011b, Maple 2014 and we was also concerned with the approximations errors and determine their implementations costs (run time and internal memory used).

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This book is designed as an advanced guide for numerical methods in the science. It covers many topics of practical numerical methods applied in the science: solutions of equations with one variable: bisection, secant, false rule, Newton-Raphson, fixed point, etc., solution of systems of equations: Gauss, Gauss-Jordan, Cramer, Inverse Matrix, Jacobi, Gauss-Seidel, Gauss-Seidel with relaxation, etc., polynomial interpolation: Lagrange interpolation, Newton interpolation, interpolation with equidistant spaces, etc., the method of the least square method for a polynomial fit (regression analysis), etc., numerical derivatives, finite differential discretization of the derivative, numerical integrations: trapeze method, Simpson 1/3, Simpson 3/8, differential equations: Euler, Runge-Kutta, differential equations with boundary values, etc. It is included the deduction of many formulas in order to clear the concepts of the numerical methods applied in Science. It is hoped that this book fills all needs of the students to get the fundaments of the numerical methods and to achieve the interest and motivation of the students for this topic.

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The present book discusses the heat and mass transfer effects on two-dimensional steady(or unsteady) free (or mixed) convection flow of an incompressible electrically conducting fluid past a stretching sheet or vertical plate or horizontal surface or continuous moving surface bounded by porous medium(or non-porous medium), in the presence of various effects such as MHD, thermal radiation, heat generation/absorption, thermophoresis, chemical reaction, Joule heating and viscous dissipation, thermo-diffusion and diffusion-thermo. The book is divided into six chapters. The governing equations of the flow under consideration were solved with the appropriate boundary conditions by using Runge-Kutta fourth order method along with shooting technique or regular perturbation technique.

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