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This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions. At the interface between the phases (in the classical problem) the temperature is set to the phase change temperature. To close the mathematical system a further equation, the Stefan condition, is required. This is an energy balance ...
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
Farlow is the author of several books in mathematics, including Partial Differential Equations for Scientists and Engineers (Wiley, 1982; Russian translation, Moscow: Mir, 1985; Dover, 1993) [3] Applied Mathematics for Management, Life Science, and Social Science (with Gary M. Haggard, Random House, 1988)
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages).
Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation. The method is to reduce a partial differential equation (PDE) to a family of ordinary differential equations (ODE) along which the solution can be integrated from some initial data ...
In many practical partial differential equations, one has a term that involves derivatives (such as a kinetic energy contribution), and a multiplication with a function (for example, a potential). In the spectral method, the solution ψ {\displaystyle \psi } is expanded in a suitable set of basis functions, for example plane waves,
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