Abstract
The well known relation between some matrix iterative methods for the solution of elliptic partial differential equations and time dependent parabolic equations is extended to establish a correspondence between the Chebyshev semi-iterative method and a time dependent hyperbolic equation. The method of "dynamic relaxation" based upon finding the transient solution to the corresponding dynamical system of equations is shown to be an exact analogue of the Chebyshev method provided the appropriate choice of inertia and damping coefficients is made. The possibility of developing further techniques based upon different physical models and leading to improved convergence is noted.
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