A NEW DIFFERENTIAL TRANSFORMATION SCHEME FOR SOLVING MANY-INTERVAL BOUNDARY VALUE PROBLEMS WITH ADDITIONAL TRANSMISSION CONDITIONS

The main goal of this paper is to investigate a new class of boundary value problems (BVPs) that are defined on a finite number of separated intervals, and the solutions defined in these intervals are connected with transmission conditions. We will call such problems as many interval boundary value transmission problems (MIBVTPs). It is obvious that MIBVTPs are much more complicated to solve than classical single-interval BVPs. In this paper, we propose a new generalization of the well-known differential transform method (DTM) to solve MIBVTPs (for the proposed generalization of DTM, we will use the abbreviation GDTM). Two MIBVTPs are solved by the proposed GDTM. The calculated approximate solutions are compared with the exact solutions graphically. The results obtained demonstrate that the GDTM is an efficient method for solving MIBVTPs.