Euler’s equation

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  • This study presented the implementation of some typical finite difference schemes solving the compressible Euler equations. As categorized in, the numerical methods will be studied are the Flux Difference scheme, whose Roe’s Approximate Riemann Solver is the representative; the Flux Vector Splitting scheme, whose Steger-Warming method is the representative; the Flux Limited Method.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Note on the Relaxation-Time Limit of the Isothermal Euler Equations

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  • An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids.

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  • Tham khảo sách 'numerical methods for ordinary differential equations butcher tableau', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.

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  • n mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below).[1][2] The derivatives are ordinary because partial derivatives only apply to functions of many independent variables (see Partial differential equation).

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  • Here follows the continuation of a collection of examples from Calculus 4c-1, Systems of differential systems. The reader is also referred to Calculus 4b and to Complex Functions. We focus in particular on the linear differential equations of second order of variable coefficients, although the amount of examples is far from exhausting. It should no longer be necessary rigourously to use the ADIC-model, described in Calculus 1c and Calculus 2c, because we now assume that the reader can do this himself....

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  • We have attempted to write a concise modern treatment of differential equations emphasizing applications and containing all the core parts of a course in differential equations.Asemester or quarter course in differential equations is taught to most engineering students (and many science students) at all universities, usually in the second year. Some universities have an earlier brief introduction to differential equations and others do not. Some students will have already seen some differential equations in their science classes.We do not assume any prior exposure to differential equations.

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  • In this paper, a new approach for solving space fractional order diffusion equations is proposed. The fractional derivative in this problem is in the Caputo sense. This approach is based on shifted Chebyshev polynomials of the fourth kind with the collocation method.

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  • Trong chương 3, ta đã nghiên cứu việc thiết lập hệ ph-ơng trình động học của robot thông qua ma trận T6 bằng ph-ơng pháp gắn các hệ toạ độ lên các khâu và xác định các thông số DH. Ta cũng đã xét tới các ph-ơng pháp khác nhau để mô tả h-ớng của khâu chấp hành cuối nh- các phép quay Euler, phép quay Roll-Pitch và Yaw .v.v...Trong ch-ơng nầy chúng ta sẽ tiến hành giải hệ ph-ơng trình động học đã thiết lập ở ch-ơng tr-ớc nhằm xác định các biến trong bộ thông số Denavit -...

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Scaling limits of non-isentropic Euler-Maxwell equations for plasmas

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  • The present volume, compiled in honor of an outstanding historian of science, physicist and exceptional human being, Sam Schweber, is unique in assembling a broad spectrum of positions on the history of science by some of its leading representatives. Readers will find it illuminating to learn how prominent authors judge the current status and the future perspectives of their field. Students will find this volume helpful as a guide in a fragmented field that continues to be dominated by idiosyncratic expertise and still lacks a methodical canon.

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  • The rest of the paper is organized as follows. Section I lays out the household’s consumption and portfolio choice problemwith a durable consumption good and derives the Euler equations. Section II describes the consumption data used in the empirical work. The service f low for durable goods (as defined in the national accounts) is more cyclical than the service f low for nondurable goods and services. The high cyclicality of the service f low, rather than durability of the good, is the key ingredient in explaining the known facts about expected stock returns....

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  • Transonic flow is a mixed flow of subsonic and supersonic regions. Because of this mixture, the solution of transonic flow problems is obtained only when solving the differential equations of motion with special treatments for the transition from subsonic region to supersonic region and vice versa. We built codes solving the full potential equation and Euler equations by applying the finite difference method and finite volume method, and also associated with software Fluent to consider the viscous effects.

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  • The main objective of the present paper is to study the transverse vibration of the prestressed beams. The differential equation of the transverse vibration of the Euler-Bernoulli beam is developed, in which the initial axial strain in every cross section of the beam is taken into account, so that the initial normal stress is not equal to zero. We have proposed some formulae to determine the natural frequencies of the prestressed beam.

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  • R Huang worked the p-elastic in a Riemannian manifold with constant sectional curvature. In this work, we solve the Euler-Lagrange equation by quadrature and study the Frenet equation of the p-elastica by using the Killing field in the three dimensional Lorentzian space forms.

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  • The paper presents a complete generalized procedure based on the Euler-Lagrange equations to build the matrix form of dynamic equations, called dynamic model, for robot manipulators. In addition, a new formulation of the Coriolis/centrifugal matrix is proposed. The link linear and angular velocities are formulated explicitly. Therefore, the translational and rotational Jacobian matrices can be derived straightforward from definition, which make the calculation of the generalized inertia matrix more convenient.

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  • The present problem deals with the thermo-elastic interaction of a gold nano-beam resonator induced by ramp-type heating under the two temperature theory of generalized thermoelasticity. The governing equations are constructed in the context of two-temperature three-phase-lag model (2T3P) and two-temperature Lord-Shulman (2TLS) model of generalized thermoelasticity.

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  • In this paper, a full dynamic model of tractor semitrailer is developed based on Multi-body System Method and Newton-Euler equations. The rollover condition is based on the load transfer ratio which correspond to the load transfer between the left and the right sides of the vehicle. This model is applied to determine the rollover condition of the tractor semitrailer while turning maneuvers on the high forward speed.

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  • This paper focuses on building a theoretical method, based on the calculation of hydraulic losses to predict the energy performance of a Low-specific speed Pump as Turbine (PaT) quickly and accurately that supported for the PaT’s impeller design. The Euler equation is built with the analysis of hydraulic loss calculation and flow phenomena passing on the machine. The trust of this approach is validated by comparing with the available experimental data.

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