The use of sucker-rod pumping systems is the most common method of artificial lift in the oil-well industry. In this work, the viscous-damped-wave equation model has been developed to describe the rod-string dynamical behavior at various well depths utilizing the inputs of load and position originating from the surface-card measurement. In contrast to the existing solutions of viscous-damped-wave equation dynamics, which is based on Fourier series truncation and finite difference method, in this paper a novel technique is presented and utilized in the real time estimation framework. In particular, an infinite-differential state space representation of the viscous-damped-wave equation dynamics is developed based on appropriate boundary transformation. The spectral decomposition and truncation of an infinite number of modes is realized, so that the partial differential equation model is cast to the system of coupled ordinary differential equations, which can be solved in real time and utilized for period and non-periodic motion stroke. Finally, the new method is validated by the real case study associated with the existing well.