Numeric-analytic solutions of mixed-type systems of balance laws

The aim of the present analysis is to apply two relatively recent methods, reduced differential transform method (RDTM) and differential transform method (DTM), for the solution of balance law systems. New generalized transformed formulas are derived. The new approaches provided the solution in the form of a rapidly convergent series with easily computable components in the RDTM case, and costly components for the DTM. A comparison between the two methodologies shows that the RDTM is more effective, efficient, powerful and able to be applicable for large class of nonlinear partial differential equations than the DTM. Two test modeling problems are discussed to illustrate the effectiveness and performance of RDTM.