A reduced order extrapolating technique of solution coefficient vectors to collocation spectral method for telegraph equation

In this article, we mainly develop a reduced order extrapolating model for the solution coefficient vectors of the classical collocation spectral (CCS) scheme to the two-dimensional (2D) telegraph equation by means of a proper orthogonal decomposition (POD). Therefore, we first present the CCS scheme, offer the existence, stability, and error estimates to the SC solutions, and rewrite the CCS scheme into a matrix-form. We then build a reduced order extrapolating collocation spectral (ROECS) model and analyze the existence and stability as well as errors of the ROECS solutions by some matrix tools. We finally verify the reliability and validity of the ROECS model by means of two sets of numerical simulations for the magnetic field produced by two parallel wires with the same voltage.