Infinite Set of Equations
نویسنده
چکیده
The paper deals with t he relative convergence of a d oubly-infini te set of equations pertaining to a boundary value problem in a waveguide. It is shown that the solution for t he equations converges differently for different choices of the co mbination of t he number of equations from the two sets. This is demonstrated by st udying t he co nvergence proper ties of t he truncated set of equations as t he number of equations is made indefini t ely largc. It is proven t hat t he solution for the reflection coeffi cient becomcs identical with t he exact solu t ion only with a p ar ticular choice of the ratio of t he equations. Thi s choice of t hc unique ra t io is also shown to be consistent with t he edge condi tion.
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