Titlebook: Computational Physics; An Introduction Franz J. Vesely Book 1994 Springer-Verlag US 1994 computational physics.differential equation.mechan

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Springer-Verlag US 1994

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N. Viswanadham,Roshan S. GaonkarLet .(.) be a continuous function of one variable. The values of this function are given only for discrete, and equidistant, values of .:

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Supply Chain Balanced ScorecardEntering now the vast field of partial differential equations, we immediately announce that our discussion shall be restricted to those types of equations that are of major importance in physics. These are the ., which may be written in the general form . (“Quasilinear” means that the second derivatives of u appear in linear order only).

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https://doi.org/10.1007/978-3-322-84533-7The flow field .(., .) in a compressible viscous fluid obeys the equation of motion . with . denoting the viscosity, and the Navier-Stokes tensor . defined by . (The coefficient in the last term is dependent on dimensionality; in two dimensions it is 1 instead of 2/3.)

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Linear AlgebraBy the introduction of finite differences a function .(.) depending on a single variable is converted into a table of function values. Such a table may be interpreted as a vector . ≡ (..; . = 1,..., .). Similarly, a function of . variables may be tabulated in the format of a matrix:

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Partial Differential EquationsEntering now the vast field of partial differential equations, we immediately announce that our discussion shall be restricted to those types of equations that are of major importance in physics. These are the ., which may be written in the general form . (“Quasilinear” means that the second derivatives of u appear in linear order only).