The 2-D Poisson Problem
نویسنده
چکیده
To compute an approximation solution to this problem, we define a discrete mesh of points (xi; yj) on which we will approximate u. To keep things simple, we will assume that the mesh is uniformly spaced in both the x and y directions, and that the distance between adjancent mesh points is h. That is, xi+1 xi = h and yj+1 yj = h. We can then use a simple centered-difference approximation to the derivatives in Equation 2 [IK66] to get u(xi+1; yj) 2u(xi; yj) + u(xi 1; yj) h2 + u(xi; yj+1) 2u(xi; yj) + u(xi; yj 1) h2 = f(xi; yj) (3)
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