Main Define Filter Select Notation Conventions Reference Solutions Similar Web Sites About cookies Conventions, Notations and Terminology For many problems with a known exact solution, the right hand side of the differential equation is given as f (or f1 or some other related form) and the right hand side of the boundary condition is given as g (or a related form). In this case the right hand side is determined by applying the operator to the exact solution. Poisson's Equation (in 2D) is -uxx - uyy = f, with the obvious modifications for other numbers of dimensions. Laplace's Equation is Poisson's Equations with f = 0. The Dirichlet boundary condition is u = g. The Neumann boundary condition is ∂u/∂n = g where n is the outward unit normal. The natural boundary condition for (for example) -∇·(p∇u)=f is p∇u·n=g where n is the outward unit normal vector. When p=1, the natural boundary conditions are Neumann. The unit interval is (0,1). The unit square is (0,1)X(0,1). The unit cube is (0,1)X(0,1)X(0,1).

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Date created: May 16, 2013 | Last updated: March 16, 2018    Contact: William Mitchell, Home Page
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