General solution of cable theory with both ends sealed.
General solution of the cable theory with both ends sealed when injecting an arbitrary current at an arbitrary point of the cable is presented, which is a time-dependent transient solution. The solution is an infinite series, each term of which is the product of a cosine term including a position variable only and an exponential term including a time variable only. The general solution contains almost all solutions reported hitherto as particular cases and the mutual relations among the various solutions of quite different forms are clarified by this general solution. Moreover the shorter the cable becomes, the more rapidly this solution converges, therefore it is useful for an analysis of the short cable in the case where the relative deviation error may grow large. The truncation error can also be estimated as the solution is an infinite series of simple functions.
D000818:Animals; D004594:Electrophysiology; D008433:Mathematics; D008566:Membranes / Q000502:physiology; D008959:Models, Neurological; D009412:Nerve Fibers / Q000502:physiology*