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In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can move with time.
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.
An Introduction to Differential Equations and Their Applications (McGraw Hill, 1994; Dover, 2006) Differential Equations and Linear Algebra (with James E. Hall, Jean Marie Mc Dill, and Beverly H. West, Prentice Hall, 2002) Paradoxes in Mathematics (Dover, 2014) [4] Advanced Mathematics: A Transitional Reference (Wiley, 2020) He is also the ...
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
Partial differential equation. Nonlinear partial differential equation. list of nonlinear partial differential equations; Boundary condition; Boundary value problem. Dirichlet problem, Dirichlet boundary condition; Neumann boundary condition; Stefan problem; Wiener–Hopf problem; Separation of variables; Green's function; Elliptic partial ...
Taylor, Michael E. (2011), Partial differential equations I. Basic theory, Applied Mathematical Sciences, vol. 115 (2nd ed.), Springer, ISBN 978-1-4419-7054-1. Zimmer, Robert J. (1990), Essential results of functional analysis , Chicago Lectures in Mathematics, University of Chicago Press, ISBN 0-226-98337-4 .
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
[1] In finite-element analysis , the essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation. [ 2 ] The dependent unknown u in the same form as the weight function w appearing in the boundary expression is termed a primary variable , and its specification constitutes the essential or Dirichlet ...
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