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We must use Iterative methods to solve the linear equations coming from solution of large elliptic equations (Laplace's equation in example we will study)
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We can motivate iteration by studying an "artificial" diffusion equation
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subject to y having same boundary conditions (in x for all "artificial time" t ) as original equation
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that we needed to solve
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Consider ANY trial function y = y(0) at t = 0
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Then we solve (*) and look at converged solution as t
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As
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The iteration of (*) in t gives a solution of (**) in limit of infinite t
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Secs 457.9