Algorithms for Calculating Eigenvalues of Initial Boundary Value Problems Defined on Connected Graphs with Changing Edges

The development of new technologies in science and engineering has led to a need for mathematical methods to efficiently calculate the eigenvalues of partial differential operators on graphs with time-varying geometric parameters. The paper presents algorithms developed using the example of canonical parabolic partial differential equations to compute their eigenvalues. The analytical formulas obtained from these algorithms can approximate the eigenvalues at specific time points.