Real-Time Solutions of Time-Varying Separable Integral Equations (TVSIE) Using Zhang Equivalency

As technology rapidly increases, the integral equation becomes an important mathematical tool to solve different problems. In addition, the time-varying problems are also one of the current research focuses, and Zhang equivalency (ZE), proposed by Zhang et al, is an effective theory to solve time-varying problems. In this paper, we concentrate on the time-varying separable integral equation (TVSIE) to verify the feasibility and superiority of ZE. To begin with, we present our general problem formulations, and then, we introduce the concept of ZE and the generation of ZE solutions. Moreover, we present two examples (i.e., one with a convergent analytical solution and another with a diverging analytical solution) and conduct two groups of numerical experiments to show the performance of ZE. Finally, we further present another two examples (being more complex and without analytical solutions) and their numerical experiments to substantiate the advantage of ZE.