The relevance of the study is due to the need to obtain analytical expressions of approximate solutions to complex technical problems, the mathematical description of which leads to boundary value problems for systems of differential equations in network-like domains and, in particular, on graphs. The article presents the formulation of an initial boundary value problem for an inhomogeneous continuum transfer equation in an n-dimensional network-like region. In the case of n=1, a symbolic method for solving the initial boundary value problem under consideration on a tree graph is proposed. The algorithm is based on the approximation of the partial derivative with respect to a time variable by a difference ratio (a two-layer approximation scheme is used) and the subsequent application of the Laplace transform to the resulting differential-difference system. A block diagram of the algorithm is presented, and a description of the structure of the software package based on the developed algorithm is given. The software package is developed in the Java programming language. To enter the initial data of the initial boundary value problem and output the solution, the web interface of the software package based on the Spring framework is used. To illustrate the operation of the software package, an example of solving an initial boundary value problem with a step-by-step demonstration of the calculation results is considered. The materials of the article are of practical value for specialists in the field of analysis of applied problems of network hydrodynamics, thermal engineering, as well as analysis of diffusion processes in biophysics.