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PoissonSolver

v20	v21
13	13	where u is the dependent variable we are solving for, and f is the forcing term.
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15		The solution to this equation needs to simultaneously 1) satisfy this equation at all points within a bounding region and 2) satisfy the boundary conditions on that region. This then lends an "instantaneous" feel to the system, much different than the wave-like solutions of hyperbolic equations which travel with finite speed.
	15	The solution to this equation needs to simultaneously 1) satisfy this equation at all points within a bounding region and 2) satisfy the boundary conditions on that region. This then lends an "instantaneous" feel to the system, much different than the wave-like solutions of hyperbolic equations which travel through space with finite speed.
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17	17	In fact, apart from their classification as either a boundary value problem for the elliptic equation, or initial value problem for the hyperbolic, they can be considered of either a "time-evolution" or "static" nature. This is a more helpful classification in terms of designing numerical methods to solve these different types of equations (see Fortran Numerical Recipes, Press et al, Vol. 2, Chapt. 19 - Partial Differential Equations). The following figure from that book illustrates this concept: